How do you write a polynomial equation of least degree given the roots -2, -0.5, 4?

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How do you write a polynomial equation of least degree given the roots -2, -0.5, 4?

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Answer 1 · 2017-09-22T12:31:10

$p (x) = 2 x^{3} - 3 x^{2} - 18 x - 8$ $p(x)=2x^3-3x^2-18x-8$

Explanation:

$given the roots of a polynomial are$ $"given the roots of a polynomial are"$

$x = a, x = b, x = c, x = d$ $x=a,x=b,x=c,x=d$

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

$(x - a), (x - b), (x - c) and (x - d)$ $(x-a),(x-b),(x-c)" and "(x-d)$

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

$p (x) = (x - a) (x - b) (x - c) (x - d)$ $p(x)=(x-a)(x-b)(x-c)(x-d)$

$here x = - 2, x = - 0.5, x = 4 are the roots$ $"here "x=-2,x=-0.5,x=4" are the roots"$

$\Rightarrow (x + 2), (x + 0.5) and (x - 4) are the factors$ $rArr(x+2),(x+0.5)" and "(x-4)" are the factors"$

$\Rightarrow p (x) = (x + 2) (x + 0.5) (x - 4)$ $rArrp(x)=(x+2)(x+0.5)(x-4)$

$\Rightarrow p (x) = 2 x^{3} - 3 x^{2} - 18 x - 8 possible polynomial$ $color(white)(rArrp(x))=2x^3-3x^2-18x-8" possible polynomial"$

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How do you write a polynomial equation of least degree given the roots -2, -0.5, 4?

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