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12 May, 22:35

What polynomial has roots of - 4,-1, and 6?

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  1. 12 May, 23:13
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    A polynomial with the roots r1, r2 and r3 has factors of

    (x-r1), (x-r2) and (x-r3) in it, it can be written in form

    c (x-r1) ᵃ (x-r2) ᵇ (x-r3) ⁿ

    where c is a constant and a, b, and n are the powers

    so roots of - 4,-1 and 6 are factors of

    (x - (-4)) (x - (-1)) (x-6) = (x+4) (x+1) (x-6)

    in expanded form

    x³-x²-26x-24
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