How do you find a polynomial function that has zeros -4, 5?

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How do you find a polynomial function that has zeros -4, 5?

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Answer 1 · 2017-12-08T20:45:40

$p (x) = x^{2} - x - 20$ $p(x)=x^2-x-20$

Explanation:

$given the zeros of a polynomial x = a and x = b$ $"given the zeros of a polynomial "x=a" and "x=b$

$then the factors of the polynomial are$ $"then the factors of the polynomial are "$

$(x - a) and (x - b)$ $(x-a)" and "(x-b)$

$and the polynomial is the product of the factors$ $"and the polynomial is the product of the factors"$

$\Rightarrow p (x) = k (x - a) (x - b) \leftarrow k is a multiplier$ $rArrp(x)=k(x-a)(x-b)larrcolor(blue)"k is a multiplier"$

$here a = - 4 and b = 5$ $"here "a=-4" and "b=5$

$\Rightarrow (x + 4) and (x - 5) are the factors$ $rArr(x+4)" and "(x-5)" are the factors"$

$\Rightarrow p (x) = k (x + 4) (x - 5)$ $rArrp(x)=k(x+4)(x-5)$

$let k = 1$ $"let "k=1$

$\Rightarrow p (x) = x^{2} - x - 20 is a possible polynomial$ $rArrp(x)=x^2-x-20" is a possible polynomial"$

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How do you find a polynomial function that has zeros -4, 5?

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