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12 May, 00:57

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

A) x^3 - 9x^2 - 22x + 24

B) x^3 - x^2 - 26x - 24

C) x^3 + x^2 - 26x + 24

D) x^3 + 9x^2 + 14x - 24

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Answers (1)
  1. 12 May, 03:12
    0
    The correct option is C.

    Step-by-step explanation:

    polynomial has roots of - 6, 1, and 4.

    We can write it as:

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

    Now multiply the terms:

    First multiply first and second bracket:

    {x (x+6) - 1 (x+6) } (x-4)

    { (x^2+6x-x-6) } (x-4)

    Solve the like terms:

    { (x^2+5x-6) } (x-4)

    x (x^2+5x-6) - 4 (x^2+5x-6)

    x^3+5x^2-6x-4x^2-20x+24

    Solve the like terms:

    x^3+x^2-26x+24

    Hence it is proved that the correct option is C ...
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