How do you write a polynomial with roots of –1, –2, and 3?

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How do you write a polynomial with roots of –1, –2, and 3?

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Answer 1 · 2018-03-17T10:52:53

$f (x) = x^{3} - 7 x - 6$ $f(x)=x^3-7x-6$

Explanation:

$Given a polynomial with roots, say$ $"Given a polynomial with roots, say"$

$x = a, x = b and x = c then$ $x=a,x=b" and "x=c" then"$

$(x - a), (x - b) and (x - c) are it's factors$ $(x-a),(x-b)" and "(x-c)" are it's factors"$

$and f (x) = k (x - a) (x - b) (x - c) \leftarrow k is a multiplier$ $"and "f(x)=k(x-a)(x-b)(x-c)larrcolor(blue)"k is a multiplier"$

$here x = - 1, x = - 2 and x = 3$ $"here "x=-1,x=-2" and "x=3$

$\Rightarrow (x + 1), (x + 2) and (x - 3) are the factors$ $rArr(x+1),(x+2)" and "(x-3)" are the factors"$

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

$\Rightarrow f (x) = (x + 1) (x + 2) (x - 3)$ $rArrf(x)=(x+1)(x+2)(x-3)$

$\Rightarrow f (x) = x^{3} - 7 x - 6 \leftarrow is a possible polynomial$ $color(white)(rArrf(x))=x^3-7x-6larrcolor(blue)"is a possible polynomial"$
graph{x^3-7x-6 [-10, 10, -5, 5]}

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How do you write a polynomial with roots of –1, –2, and 3?

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