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12 May, 22:12

Fina a polynomial function of degree 3 with real coefficients that has - 1,2,-4 as zeros

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  1. 12 May, 22:38
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    f (x) = x³ + 3x² - 6x - 8

    Step-by-step explanation:

    given the zeros of a polynomial x = a, x = b, x = c then

    (x - a), (x - b), (x - c) are the factors of the polynomial and f (x) is the product of the factors

    here x = - 1, x = 2 and x = - 4 are the zeros, hence

    (x + 1), (x - 2) and (x + 4) are the factors

    f (x) = a (x + 1) (x - 2) (x + 4) ← a is a multiplier

    let a = 1, then

    f (x) = (x + 1) (x - 2) (x + 4)

    = (x² - x - 2) (x + 4)

    = x³ - x² - 2x + 4x² - 4x - 8

    = x³ + 3x² - 6x - 8
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