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Knowledge CheckFind a polynomial f(x) of degree 4 that has the following zeros-4, -6, 0, 5Leave your answer in factored form_...

Question

Knowledge CheckFind a polynomial f(x) of degree 4 that has the following zeros-4, -6, 0, 5Leave your answer in factored form_

Knowledge Check Find a polynomial f(x) of degree 4 that has the following zeros -4, -6, 0, 5 Leave your answer in factored form_



Answers

Find a polynomial function that has the given zeros.
0,-4,-5

All right, So we need to find a polynomial of fourth degree with integral coefficients. That has these two routes. The two routes were given our four plus three I & 5 -1. And we need to be at the fourth degree. So if you have only two routes, there should be two other routes. What could they be? Well, we had to complex roots here. And for each one of the two we need its conjugate pair to also be in the polynomial as a route. So therefore the other for the other tools are 4 -3, I And five plus I. So now it gets pretty easy. It's more to play dark. So it's X minus four plus three I times X minus Or -3, I times X minus five plus I. And eggs minus five minus I. So first two terms together and the other two terms together. And we get X squared minus eight eggs plus 16 last night Just plus 25. And for the other two terms multiplied. I get another X square minus 10 X. And plus 26. So finally I have to multiply these two terms. It's gonna give me excellent fourth. And then for the extra to a third term have a negative eight a negative 10 negative 18 XQ. And so on. If I go on for X squared term, I'm going to get it Plus 80 x squared. For negative eight X. Times negative 10 X. Then next I'm going to have last 26 and plus another 25 x squared which is 51 in total X squared. Yeah. These are going to add up to 131 export. So what's my Coefficient for X to the Power 1? Well, it's going to be negative eight X times 26 plus 25 10, negative 10 X. And adding those two will give me -580, -458 x. And lastly 25 times 26 650 Plus 650. So here's my polynomial. Let me just crest is part act. There we go. That's the final answer to make it. Need, let's rewrite it. Okay, and we're done.

Yes, we have given dig any five and Zito minus two minus one Zito one and no. According to the factor to roam the expression x minus C is ah sector off Be X if on only if b c is equal deedle Now that, uh, new men function be x so yeah, si is equal to minus two. He's, you know, be X then Shin X plus two is, uh fact at all Be X on if si is equal to minus one is ah Zito be X then the commission X plus one is ah sector all be x on If si is equal to gee toe is, uh do you know Oh, be X The addition X minus zero which is equal to X is ah, the X on Yeah, si is equal to one is Zito be X and, uh, petition X minus one is a e x on a Yeah, si is equal to oh is a little off b X then expression X minus two is a fact at all me x So the whole new milk and we do turn in the man be X is equal axe multiplied by X plus one multiplied by X minus one, multiplied by X plus two multiplied by X minus by using the identity identity. Esquire, minus B squared is equal a plus B on a minus bi it plus be prepared by a minus. Bi Biggert be access tickle toe axe multiplied by It's a squared minus one on multiplied by X squared minus food. No be accessible. Toe multiplied acts with dot minus one. We get Q minus X multiplied by for minus food, so the final result off B X is equal access to the power five minus five x cubed plus Ward X.

Yes, we have given dignity Food on Zito's minus one comma one, My mom. Right now, according to the factor to Rome, expression X minus C is fact that off be if on only if B c is equal to zero So let a polynomial function be X yeah si is equal to minus one Is 00 be X then shin X plus one is a be X Ah, If si is equal to one is Zito off? Be X, then shin X minus one is a fact that off e x on FC is three is ah Zito off E X expression X minus three is ah uh P x And if C is equal to five is ah Zito off e X, then position X minus Fife is a fact, uh, off be a now the polynomial function P x can be returned in the farm. B X is equal toe x plus one multiplied by X minus one multiplied by x minus three multiplied by x minus like on B X is equal X plus one x plus one and X minus one. This becomes identity. Be good. Glad minus one on when you multiply it X minus three with minus five. We get X squared minus five minus three X plus being no. B X is equal to when all this multiplied by the time we get, uh, simply the right X squared minus one multiplier to buy X squared minus plus 15. Now the final value B X is equal when the storm multiplied by this access to 44 minus it excuse Los 14 X Square plus 18 x minus Being

In this video, we find a polynomial f extra The following properties Police degree has integer coefficients has zeros exported 5/2 minus one and zero on If you're supposed to write the polynomial in goes factor on general for the first. Not that a either with half pepper X Kniffen horny X minus. Stay is a factor of four eggs. Be with an extra quarter 5/2 minus one and there are zeros off takes. So the confident that x minus 5/2 x minus minus one on X or factors off politics since ever fixes off least degree the power off. All factors are record toe one more or since their coefficients are major, you multiply the factor X minus 5/2 by two and consider to explain its five as a factor off off eggs therefore off. X is equal to two times X minus five times X minus minus one times X, which usually cuatto two times X cubed, minus three times X x squared, minus five times X There for this factor. Form off Heartbreaks is according based Times two X minus five times X plus one on real general for music or go to X cubed minus three to sport minus five x. I hope you enjoy watching this video and time sport.


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