5

What are all the possible rational roots of f(e) = 224 + 23 + 4?0,+3,11,12,+4 1l,+2,+40,+1,12,+4+3,11,12,+4...

Question

What are all the possible rational roots of f(e) = 224 + 23 + 4?0,+3,11,12,+4 1l,+2,+40,+1,12,+4+3,11,12,+4

What are all the possible rational roots of f(e) = 224 + 23 + 4? 0,+3,11,12,+4 1l,+2,+4 0,+1,12,+4 +3,11,12,+4



Answers

List all possible rational roots for each equation. Then use the Rational Root Theorem to find each root.
$$
3 x^{3}-5 x^{2}-4 x+4=0
$$

Okay, So to start out finding all the possible rest rational solutions. Um, to this polynomial, we are gonna list out the devise er's for four. Not too hard there. Just one to and before then, we're gonna list out all of the devices for six. They're just one to three and six. So the rational roots here, um, just tells us that any rational solutions to this polynomial will have one of these as the denominator and one of these as the numerator. And the sign can be positive or negative. It's a little confusing, but let's just get started. So for the first round of denominators that we're all gonna have there are gonna be one. So it's right that out 1111 And the numerator are gonna be the 1st 1 of these values. So you could be 1/1 to over one 3/1, or it's 6/1. And now let's do that for two as the denominator using two is the denominator in the numerator Kita be one to three or six, most of it one more time. With Fouras, The denominator numerator could be one to three or six Now let's simplify these down a bit. 1/1 just equals 12 over once equals 2311 equals 36 Everyone equal six. 1/2 is just 1/2. And to everyone, XXI actually equals one, which we already have. We're gonna cross that one out. 3/2 is just stays 3/2 and 6/2 equals three, which we already have. So we can cross that one out. We have 1/4 of it to over four was 1/2. So we can cross that one up already accounted for. 3/4 is just three points and 6/4 is three halves, which we already have. So listen up, all apostle Russian low sluices. We have positive or negative one positive. Negative too positive or negative. Three positive or negative? Six Positive or negative 1/2 positive or negative? Three. Halfs, Positive or negative? One fourth Positive or negative? 3/4 And there we go

Uh huh. So for this question, we have our constant form equals to fool. And we have our leading coefficient vehicle to one year. So our numerator should be the factor of food that is plus minus one plus miners to plus minus four. Yeah, And also for the denominator, we'll have last 10 men is one. So we have X equal to platform. Manage. One platform managed to I am platter man is full. And then we take all this possible rules into our equation. So we are Equation is X to the power of three plus x choir plus four x plus four echo two barrel and then we try. Mhm. X equals one. Here we'll have one plus one plus four. Last 4000 equals to zero and minus one. We'll have minus one. That's one minute four Plus for that help you asked. Zero. And so we are sure that he's our roots now and then with tax. Okay to that, have you us eight plus four plus eight class before Nichols who and then he talked to zero. And also we are fun because they are all, uh how to two terms. So that won't be zero, and then we try minus four manor to here we are. How? Minus eight Last four minus eight plus also Dublin Echo 20 and my notes. Food that will give us 60 for manners plus 16, nine of 16 last four other equals to zero. So we have our answer. Our route here is X equals two minus one.

And this problem well defining all possible lash numbered and it's actually our shoulders. Using irrational, rich zero, we can find that the possible rational roots are the plus minus. Oh, the factors, um 15. Which is the constant over factors of eight, which is the leading coefficient. So this is the close of plus or minus off. 13 five and 15 over 1248 So this when we simplified it, it would be, Ah, the poster minus of 1 1/2 1/4 one a three 3/2 3/4 three a Clive five over five halfs. Five fours Y es 15 15 halfs, 15 fours, 15 8 So these are all the possible, uh, rush over its of this equation. Uh, now we can to find the actual rational routes, we can plug these, and but because these because this will be time consuming, we will only check the three that are the roots. So we will check X equals negative one. How for this? Uh, we do eight times negative. 18 minus 28 times 14 plus 14 times negative. 1/2 coast, 15 40 naked of one minus seven minus I've been close to 15. Uh oh, yeah. We don't know if this is equal to zero yet, and this is indeed zero. So X is 1/2 X equals one negative. 1/2 is irrational. Now we will check X equals three. How so? A times 27 over a minus 28 times nine of before, plus 14 over 14 times. Three over two, close to 15. This will be 27 63 21 close to 15. And, um, this this And this week 0 63 This also equals zero so X, because thrilled to is also a rational. The last one we will check is X equals bye. Huh? So a ton 1 25 over eight. Minus 28 times 25 over four, most 14 times. Five over to close 15 equal zero. This will be 1 25 Um, this will be negative. 1 75 just will be 35. And this will be 15. Um, this post this plus this equals 1 75 So 1 75 minus 1 75 0 So, uh, X equals viable for two is also a rational. So the answer to this problem would be that X equals negative. 1/2 three over two and Bible for two are the rational actual roots off this equation.

Were asked to find the possible combination of real and imaginary roots for this polynomial. Our degree is four fours are highest. Excellent. So we're gonna have four complex roots, meaning the total number of routes we're gonna have this for So are really roots. Plus, our imaginary roots have to equal for an imaginary roots must come in pairs. That's key conjugated pairs. So the numbers in the imaginary column must be. Even so we could have zero imaginary routes to imaginary roots for four imaginary roots. Because we have four total, we can't go any higher than that. Four total means if we have zero imaginary for we must have four riel to imaginary. We must have to riel for imaginary. We must have zero riel, so these are possible combinations of real and imaginary roots. Given that we have four complex roots now, the last thing we need to do is find the possible railroad rational roots. So our rational roots means we take the factors of our constant 26 and divide those by the factors of our leading coefficient. So the factors of 26 are plus or minus one closer, minus two plus or minus 13 and plus or minus 26 and our leading coefficient factors. The factors of two are just plus or minus one or plus or minus two. So any of these ratios, for example, negative 13 divided by positive one. Negative 13 is a possible rational route for this equation. Um, but we would have to check all of these roots, but it helps us to narrow the possible routes down toe only a handful, as opposed to all real numbers.


Similar Solved Questions

5 answers
6310 Ex?of Hechnology 3etics4( Spt) Find the reduced Low _ ehelol E YOUI IOw forT of the operations, ULLIIC >5(5pt) . The linear system ATCx = A-1 =[ C-'such that nndnonsingular , with Find tke solutionand b
6310 Ex?of Hechnology 3etics 4( Spt) Find the reduced Low _ ehelol E YOUI IOw forT of the operations, ULLIIC > 5(5pt) . The linear system ATCx = A-1 =[ C-' such that nnd nonsingular , with Find tke solution and b...
5 answers
(8) A student states: If the series 5=l 0r converges then Er-1 la, | converges _ Which of the following makes this statement false? (5~= (B) E;=1 (C) E;=1f05 (05= (E) None of theseFor number 9 _ 11, do the following series (A) Converge absolutely (B) Converge conditionally (C) Diverge(95e(-1)"a(10) Er=o(-1)" ()
(8) A student states: If the series 5=l 0r converges then Er-1 la, | converges _ Which of the following makes this statement false? (5~= (B) E;=1 (C) E;=1f05 (05= (E) None of these For number 9 _ 11, do the following series (A) Converge absolutely (B) Converge conditionally (C) Diverge (95e(-1)&qu...
5 answers
Li the H compounds order of increasing 8 reactivity 2 electrophilic
li the H compounds order of increasing 8 reactivity 2 electrophilic...
5 answers
[21(203: 44 107) 4#04 x4 41*8*8847 Exhah z %oi 824 9. k*} 4#01 mt = 3u{(-1)*+2 '-') (k=1,2, 2 Zorl= %&9 C8 & #il9/at: (a) X 4 464584 (b) X 4 r6=1,2,_)* +8
[21(203: 44 107) 4#04 x4 41*8*8847 Exhah z %oi 824 9. k*} 4#01 mt = 3u{(-1)*+2 '-') (k=1,2, 2 Zorl= %&9 C8 & #il9/at: (a) X 4 464584 (b) X 4 r6=1,2,_)* +8...
5 answers
Vea tha givan praphs of x = f(t) and y = o/t) sketch Ihe corresponding carametric cunn ue ry-plane.Ane nne ntekerch belr
Vea tha givan praphs of x = f(t) and y = o/t) sketch Ihe corresponding carametric cunn ue ry-plane. Ane nne ntekerch belr...
5 answers
1 1 Rate = thls 11 2 N,O5{9) 3 was studled1 @xpertent temperalure Huct 2 1 Jollotng 6 [C_(0)] {0} resuits; 1 1 ilu
1 1 Rate = thls 1 1 2 N,O5{9) 3 was studled 1 @xpertent temperalure Huct 2 1 Jollotng 6 [C_(0)] {0} resuits; 1 1 ilu...
5 answers
Design of two-way supported slab panel No 3 in the figure below by using coefficients merthod (CF). Use vairable S= 4 m; and F= 7 m the slab thickness is 200 mm. if the dead load i5 10 kN/m2 (not including se Live load is 2 kN/m2 fc' = 28 Mpa and fy =420 Mpa. density of concrete is 25 kN/m? the answer should be baked with slab layout to show reinforcement in both directionsall columns300 mm X 300 mm
Design of two-way supported slab panel No 3 in the figure below by using coefficients merthod (CF). Use vairable S= 4 m; and F= 7 m the slab thickness is 200 mm. if the dead load i5 10 kN/m2 (not including se Live load is 2 kN/m2 fc' = 28 Mpa and fy =420 Mpa. density of concrete is 25 kN/m? the...
5 answers
D: Does lim f(x) exist? If so, what is it? If not why not?0 A: Yes, Iim f(x) exists and equals X-6 Yes lim f(x) exists and equals 8 x-6 lim flx) does not exist because Iim f(x) lim f(x): 736 X-6 " X6 0 D. No, lim flx) does not exist because f(6) is undefined X-6
d: Does lim f(x) exist? If so, what is it? If not why not? 0 A: Yes, Iim f(x) exists and equals X-6 Yes lim f(x) exists and equals 8 x-6 lim flx) does not exist because Iim f(x) lim f(x): 736 X-6 " X6 0 D. No, lim flx) does not exist because f(6) is undefined X-6...
5 answers
L In thel Chrom RNA Ilposomes DNA Quedton 1 Iaboratont 6 9 complex organic polymers 8 slmulatons 3 81and Urey observed Ine ablotl 1
L In thel Chrom RNA Ilposomes DNA Quedton 1 Iaboratont 6 9 complex organic polymers 8 slmulatons 3 8 1 and Urey observed Ine ablotl 1...
5 answers
According to thc American Red Cross, 10% of all Connecticut residents have Type blood_ A random sample of 22 Connecticut residents Is taken the number of CT residents that have Type blood_ of the 22 sampled What Is the standard deviation of the random variable X?v2.084808 V1.g8 V1 982378 V2.205082 V1 637858 V2.306458
According to thc American Red Cross, 10% of all Connecticut residents have Type blood_ A random sample of 22 Connecticut residents Is taken the number of CT residents that have Type blood_ of the 22 sampled What Is the standard deviation of the random variable X? v2.084808 V1.g8 V1 982378 V2.205082 ...
5 answers
A spherical conductor of charge 2q and radius Rz is wrapped by an external insulating layer charged at making it look like 3 sphere of radius Rz: What is the electric field in the white region (0 < r < Ril?RR2teo?22teoz2IteotTw R"
A spherical conductor of charge 2q and radius Rz is wrapped by an external insulating layer charged at making it look like 3 sphere of radius Rz: What is the electric field in the white region (0 < r < Ril? R R 2teo?2 2teoz2 Iteot Tw R"...
5 answers
Problem 7point) After performing a trigonometric substitution, you are left with the following integral (for some constant A) Asec3 0 d0. tan? 0 Which of the following could have been the integral that you started with before the substitution?4r2 + 5 dxdz. 5x2dz. 4x2 +55.2 dx4x2dx_x3
Problem 7 point) After performing a trigonometric substitution, you are left with the following integral (for some constant A) Asec3 0 d0. tan? 0 Which of the following could have been the integral that you started with before the substitution? 4r2 + 5 dx dz. 5x2 dz. 4x2 +5 5.2 dx 4x2 dx_ x3...
5 answers
A magazine provided results from a poll of 22 adults who wereasked to identify their favorite pie. Among the respondents, 79%chose chocolate pie. If the confidence level is 95%, calculatethe confidence interval for the proportion of adults who identifychocolate pie as their favorite pie.Enter the lower bound of the confidence interval as a percentagewithout the % sign. (Round your percentage to the nearesttenth.)
A magazine provided results from a poll of 22 adults who were asked to identify their favorite pie. Among the respondents, 79% chose chocolate pie. If the confidence level is 95%, calculate the confidence interval for the proportion of adults who identify chocolate pie as their favorite pie. Enter t...
1 answers
What is the molality of a solution prepared by dissolving 0.385 g of cholesterol, $\mathrm{C}_{27} \mathrm{H}_{46} \mathrm{O},$ in 40.0 $\mathrm{g}$ of chloroform, $\mathrm{CHCl}_{3} ?$ What is the mole fraction of cholesterol in the solution?
What is the molality of a solution prepared by dissolving 0.385 g of cholesterol, $\mathrm{C}_{27} \mathrm{H}_{46} \mathrm{O},$ in 40.0 $\mathrm{g}$ of chloroform, $\mathrm{CHCl}_{3} ?$ What is the mole fraction of cholesterol in the solution?...
2 answers
Craphs "10ptsl Coustrci graph with Hamniitunt path possible? (Your graph must be counccted SublEuler path wich vcrtacs bipartite uudlirected).
Craphs "10ptsl Coustrci graph with Hamniitunt path possible? (Your graph must be counccted Subl Euler path wich vcrtacs bipartite uudlirected)....
5 answers
J3;; 1 1 11;
j3;; 1 1 1 1;...
5 answers
The field below accepts list of numbers or formulas separated by semicolons (e.g: 2; 4; 6 or € + 1; € _ 1). The order of the list does not matter:
The field below accepts list of numbers or formulas separated by semicolons (e.g: 2; 4; 6 or € + 1; € _ 1). The order of the list does not matter:...

-- 0.021050--