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Find all of the roots, real andlor imaginary, of h(r) Show all ofyour work 2 4 7x 3 hc-yx 4 Zxs 6X...

Question

Find all of the roots, real andlor imaginary, of h(r) Show all ofyour work 2 4 7x 3 hc-yx 4 Zxs 6X

Find all of the roots, real andlor imaginary, of h(r) Show all ofyour work 2 4 7x 3 hc-yx 4 Zxs 6X



Answers

Find all of the real and imaginary zeros for each polynomial function. $$h(x)=x^{3}-x^{2}-7 x+15$$

You never give in and use the power of excess for plastics X squared minus 78 people to do. We'll solve the middle off X from this prison. First of all, it will convert the give Vinick with inequality. So how we can convert. Let's see here let excess quite physical, Duke. Why no blood in the place of eco squad? Why here? Then it will get here. Why? Yes. Square last six way minus seven is going to do now. This is that wonder Dickie with him. Now we can try this aggressive using the picture. I just met her in the place up six way weekend. I here bless seven way minus way minus seven is able to, you know, take the common Why from the past Kutan. Then you can right here tryinto by Bless Simon. Now take the minus one common from the last photo. Why pillars? Same unethical to do not take the common y plus seven from Haltom. After taking common here, they get by minus one is goingto do. Now we have a two picture by plus seven and my minus one. So either by plus seven is Geo Are y menos Ebony do so here, Michaela. Seven It tickle. Kojiro O R y minus one is able to do from here. We'll get the Baluch wise minus seven are Why did you do what? No luck in the blue boy here. Excess critical Do minus 70 r. Exercise will do. Well, no, I think that's quite rude. Hey, then you will get exits. Kal toh. Blessed, Minus grouped under minus seven Are its physical to bless. Minus good. Under what? And they want to take this quiet, But we have to write books and plus minus here. No, we can I bless. Minus Who'd under seven in tow? My nestling. Yeah, it's it's gonna do Is quiet off below one, each less minus one. Here. No, here we can. I bless. Meanest brute under Symone. I Yes, We're as you know, the bill. Oh, I guess where you could do one in complex number, you know, off ice when he minus a line in the complex number American right here. Exits going to bless minus Route seven. I So you guard here for Della? Pace is ex circle to one minus one exists called to Route seven. I explode. Do minus or similar. We can take one day with this solution. Egypt. Correct or not, and excel to one 11. Give any Grissom one the power core plus six in tow. One in the whole of square minus seven is going to do after simply because I'm here. He will get geological toe you. This district mint is true there. Say ex. It's called one. Eject Correct solution of the given. Nick, listen. Now check. Add X is going to minus one. The power off my next one. Each poor plus six in tow. Man is Veronica with the square minus seven is equal to zero here. Well, get geo physical. Do do. This statement is true. Deaths right? Exists do Minus one is a correct solution. Number given invisible. Now you can check. It is I exit. Will do room saving. I well again given prison were writing here. Steven, I coulda power food plus six in dude or seven. I get the whole square minus seven is good. You Here. You get 7 to 7 49 I get a power four plus six in tow. Seven for ditto. I s squared minus seven. It'll do you Iike a power shortage. One because I can power pole. You can do, I guess. Square in tow. I s got the better of my ex. Kaiser minus one minus one is You're gonna do what then Harry will get 49 plus 42. Well, I s quite minus one. There's one man is 42. When the seven people could you it really that minus 40? Did you know Gino? So geological, Kojiro It drew a straight man. That's why X It's called Tau seven i e. J. Correct solution, given a similar lived in check so you can get there Extra toe minus seven. I is also and excellent on that given in prison. So here you get that force, Alison off the daily living or so something. Even in prison, we're too complex and too, is it? Let me guess a region. You may not be an intelligent, really a solution. Thank you.

So we got the following polynomial. Um, and we need to find the zeros for that. So let's first start listing the factors of 24. 1234 68 12 24. The leading coefficients one. So that's just gonna be as it is here. Now, let's start. Leah writing down the coefficients 13 minus a minus 20 to end minus 24. So let's start with one. The one in one one again for So I'm using synthetic substitution here. It's minus floor. It's four minus 26. It is 26 again. This doesn't work. Now let's use to five 10 to here for negative 18 minus 36. No, Doesn't work. Trying. Negative too. That one minus two. Here of one minus two. It's minus 10 20. Okay, Scott minus two here for that does not work. Let's try three, 3136 18 10 30 eight and 24. There we go. So we have our factor here. X minus three. So that'll be X cubed. Plus six x squared plus 10 x plus eight. All right, so X minus three into X cubed plus six x squared plus 10 x plus eight. Now it's do synthetic substitution again. Here, let's list the factors of 8124 and eight and write down the coefficients 16 10 8 So let's start with one here, plus in minus here. Actually, let's start with four. It's 24 one for 10 40 50 very high. Trying negative for get one minus four to Highness Say to again minus 80 There we go. So we got X squared plus two X plus two so X minus three into X plus four. So we have our factor here. X plus four into X square plus two X plus two so X minus three X plus four X squared plus two X plus two. Now, if you put that equal to zero X is three and X's negative four. Now we cannot factor this one here, but let's check. Ah B squared minus four. A. C. Remember, A is one B is two and C is to B squared. That's four minus four times A, which is one time See, which is to this is less than zero. So X squared plus two x plus plus two is not gonna have any real roots. So you're only roots are three and negative for

It was a fatal fix. So by observation you can see that it off three is equal to zero because it off three is three Q minus three cube, which will give you 04 times three is equal to 12. 04 X minus 12 0 So it off trees, actually quarto zeros X minus three divides this polynomial. So let me compute the caution for you. And I will explain in a second why we're doing this. But let me do the long division first. Well, not in a second, but in a minute broke so x cubed, divided makes is excluded. So we get X Q minus three X square. Subtract this. You will get zero Andi for X minus trail will broke down. Four X rated wakes is four and again four X minus 34 times explains threes for X minus 12 and they remained. There has to be zero because we already know in hindsight that I have to use equal to zero. Okay, so now it's your fix is since 306 ministries obviously affect ER and by this long division, we know that it's off. X is equal to x minus three times X squared, plus food. If you want, you can open the brackets and quickly very fight. But this is what Long Division stands for. Knife Better fix has to be equal to zero. Then one of the factors have to be equal to zero. So 10 is of course, X equals three. But the other two zeros come from the factor. Expect less for equal to zero. So if X squared plus one is equal to zero, that means X squared is equal to negative food. So that means X is equal to square root off. Negative one. This is I Time square, root off four, which is plus or minus two. So you get to imaginary deeper zeros blessed way and minus TWE and one real zero bitches three.

Okay, so we have the whole equation and were asked You find of its We'll see that there's an excellent age term. So it's factor that out rough or ex word when it's for at minus six is equal to Joe and I work. In fact, throughout this term, right here where this equation that's just x and see menace for eggs. Thio. Let's see, we have three and to the multiplies six. It's sure to use the quadratic equation, so that's negative B, which is positive for plus minus the square root of B squared, which is 16 minus for a see all over two. A Mrs X is equal to So he gets. Let's see, let's find our square root valley inside 16 minus four times negative. Six. Miss, you be this great weight of 40. We get four close to madness For what? A 40 which is four times candidates. I'm to skirt of okay over too. And then we can divide. So we get two plus minus. Choose or not you, um, square it a 10. Do we get X is equal to or X minus shooting plus guru to 10 as well as thanks minus to minus grew out of 10 and it's equal to d'oh. So we have our it's X is equal to zero June plus river to 10 as well as two minus square to 10. And as we could see there not raised to any power, so they're all have a multiplicity of one.


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