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QUESTION 2Azero of the polynomial &x3-10x2-X+3 in Z15lx] is Oax-1 Ob.x-1 Ocx2 O d None...

Question

QUESTION 2Azero of the polynomial &x3-10x2-X+3 in Z15lx] is Oax-1 Ob.x-1 Ocx2 O d None

QUESTION 2 Azero of the polynomial &x3-10x2-X+3 in Z15lx] is Oax-1 Ob.x-1 Ocx2 O d None



Answers

If $P(x)$ and $Q(x)$ are polynomials, then $f(x)=P(x) / Q(x)$ is a(n) ______ function provided $Q(x)$ is not the zero polynomial.

This is problem number 61, we are given the following parameters and our task to find a polynomial that satisfies all of them using real coefficients. So to begin, we will find our factors. These are zeros. Given that we have one complex zero, we know that there is another zero, that is it's complex conjugate. So our first factor will be x minus two plus five I. Mhm. And our second factor will be X -2 minus five. I. These are all of our factors as we have a degree of two. So we're not missing any zeros and we can go ahead and expand to this. In doing so, we find the following equation X squared minus four X plus 29. Since our leading coefficient is one and that is what you're looking for. We do not need to scale this by any means. So we have reached our final solution of x squared minus four X plus 29.

We have been given BX as X cubed minus two X plus one. Okay, and one is zero. It means X minus one is the factor off. This speaks No what will first let us do it? The PX liteks minus. So it gives you X cubed minus two x plus one and he will get excess squash or becomes X cubed minus X squared. OK, and this comes out to be nothing but get plus so excess squared minus two X plus one Now go with plus X. So it gives you X Esquire minus execute and he will get minus. It'll get Plus it makes it get minus X plus one. Now what we can do, we can go Nothing but minus one. So it gives you minus X plus so vanishes. Okay, now this implies attack. Our question is nothing but two X is excess clan plus X minus one. Now what we can do let us factories it. So if you want factories it we can write it does moreover what can do you is there supply the form Love getting a quadratic equation, right? Rousseff accord Articulation. That is your row X will be nothing but a minus bi plus miners on little B squared minus four a. C. No different formula that responds to your corner. That is excess squad plus p x plus e and your Rubies like this. So if you go and find for your excess squad plus X minus one vote, we will get We will look. Something like X is equal to minus Kate Miss minus one plus minus under the B squad that is one minus four into one into minus one. Okay. And hold upon. Cooler. That's going to what for? Becomes minus one plus minus. Undercoat. It would give you one plus four. OK, I would do one plus four all about and remove. Jacket will keep with the value s minus one plus minus. Road fight fight therefore to L minus one minus five and another will lose minus one place rolled fight by Now, if you talk about these eels, you can represent your p X in the form off its factors. So it's fact that is nothing but X minus one second factor becomes X minus and minus one. Bless through five. My group and the third factor becomes ex miners minus one my list. Look. Fine. So this in this American evidently extended from 50 zeros are actually because toe one minus one plus ruled five vital and minus one on over here, we get minus and, uh, fight by. So these values the rule for a given.

We have been given PX as minus X cubed less four X squared plus seven x minus 28. And when more information is there That four is one of the Zeros. It means X -4 is the factor of P x. Okay. So if it is the factor let us go and divide PX. So we'll get tax -4 and it comes out to be minus Excuse me Plus four x squared Plus seven x and -28. Okay now what we'll do we'll go with minus access square. So it becomes minus X cubed And Plus four x square. So this particular thing will be canceled out. It becomes seven X -28. And if you go here we'll get plus seven. So it gives you seven x -28 and Italian cancer. So it means we have got the caution does minus access choir plus seven. Let us equate it to zero to get the value of X. So X gives you x squared gives you seven and it in turn gives you x is equals to plus minus Route seven. So too will lose off exa over here. Now if you write P x P x can be written as the factors product of the factors Okay, so PX is nothing but X -4 that is given in the question itself and it becomes X plus room seven and and there is x minus groups and hence the zeros of this problem becomes accessible to four comma Plus minus groups have enhanced three values of x are obtained and these three other zeros of the given cubic polynomial.

We have been given the X has X cubed minus two X squared minus five X plus six. And also we have that three is the zero. This polynomial It means if trees zero then it says that X minus three first me must be effective. Must we factor off this? So for that led us to white. So when we divide X minus three what we get is that here, execute minors. The works is squad minus five X. Let's six. No, Really good. Clear excess quest. So it becomes X cubed minus three Xs square on Diffie replacing. So this cancels out and this gives you access Squad minus five X plus six. Now it can go with plus X sold becomes access squad minus three X. Okay. And again this becomes minus. Didn't become plus on he ever get minus two X plus six Know what we can do? We can go with minus toe. So if we go with minus toe, we will get here minus two works on plus six it becomes again this castle's wholesome becomes it'll. This implies that our question our question is nothing but access Kwab plus X minus two Now what we need to do. We need to factor. I did first. Okay, so for factory cities, recognize it will get excess square. And here you get plus two eggs and minus X minus toe. Look it now. This can build and has X taken is common. We get explosive. Toe minus one taken has called an express toe. So this gives you X minus one and X plus two of what we can write. It does. We had our p x okay and p x zero That is X minus state and other zeros on nothing but your X minus one on X plus. Soapy X can be represented like this. And if you go for zeros, Zeros Okay. So really like the roses. Okay, We have already given one and minus two. So 300 miners to other required zeroes off the given polynomial.


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