Identify the simplest polynomial function having integer coefficients with the given zeros. 0,-4,√3. A. P(x) = x^4 + 4x³ – 3x² –

Question

Identify the simplest polynomial function having integer coefficients with the given zeros. 0,-4,√3.

A. P(x) = x^4 + 4x³ – 3x² -12x
B. P(x) = x^4 + 4x³ -12x² – 3x
C. P(x) = x³ + 4x² – 12x – 3
D. P(x) = x³ + 4x² – 3x – 12

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Thu Hương 5 years 2021-07-18T15:50:52+00:00 1 Answers 126 views 0

Answers ( )

  1. Nem
    1
    2021-07-18T15:52:37+00:00
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    Answer:

    x^4+x^3-3x^2-12x

    Step-by-step explanation:

    0,-4,√3 are the zeros of polynomial. P.

    If x=√3 is a zero and P has integer coefficients, then x=-√3 is also a zero. Both of these results come from solving the equation x^2=3 or x^2-3=0 so x^2-3 is a factor of P.

    x=0 is a zero, means x-0 or x is a factor.

    x=-4 is a zero, means x-(-4) or x+4 is a factor.

    So the polynomial, P, in factored form is

    x(x^2-3)(x+4)

    Let’s write in standard form.

    I will begin by multiplying the last two factors.

    x(x^3+x^2-3x-12)

    Distribute x

    x^4+x^3-3x^2-12x

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