Which second degree polynomial function has a leading coefficient of –1 and root 4 with multiplicity 2?

Question

Which second degree polynomial function has a leading coefficient of –1 and root 4 with multiplicity 2?

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Ruby 2 weeks 2021-11-22T00:45:23+00:00 2 Answers 0

Answers ( )

    0
    2021-11-22T00:46:26+00:00

    Answer:

    (x-4)^{2}

    or –x^{2}+8x-16

    Step-by-step explanation:

    Given a second degree polynomial has a root 4 with multiplicity 2

    That means, 4 is a repeating root of the polynomial.

    Any second degree polynomial has at most 2 real roots.

    ⇒Both roots of the polynomial are 4.

    and its expression can be written as(x-4)^{2} where c is a real number

    ⇒c·(x^{2}-8x+16)

    ⇒cx^{2}-8cx+16c

    Also, the leading coefficient is given as -1

    So, c = -1

    and the expression becomes (-1)x^{2}-8·(-1)·x+16·(-1)

    x^{2}+8x-16

    0
    2021-11-22T00:46:32+00:00

    The correct answer is D, or f(x) = -x^2 + 8x - 16

    Just got it right on Edge 2020, hope this helps!! 🙂

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