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21 November, 09:57

What polynomial has roots of - 5,-4 and 1

x^3+8x^2+11x-20

X^3+x^2-22x-40

x^3-x^2+22x+40

x^3-8x-11x+20

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  1. 21 November, 10:24
    0
    x³ + 8x² + 11x - 20 ← the first on list

    given the roots of a polynomial, say x = a, x = b and x = c

    then the factors are (x - a), (x - b) and (x - c)

    the polynomial is the product of the factors

    f (x) = (x - a) (x - b) (x - c)

    here x = - 5, x = - 4 and x = 1, hence factors are

    (x + 5), (x + 4) and (x - 1)

    f (x) = (x + 5) (x + 4) (x - 1) ← expanding factors gives

    f (x) = (x² + 9x + 20) (x - 1) = x³ + 8x² + 11x - 20
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