Find all the real zeros of the function : g(x) = 4 (x-1) (x²+4) (x+6) if there is more than one answer , seperate them with commase

Question

Find all the real zeros of the function : g(x) = 4 (x-1) (x²+4) (x+6)
if there is more than one answer , seperate them with commase

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Huyền Thanh 4 years 2021-07-31T20:22:40+00:00 1 Answers 15 views 0

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  1. niczorrrr
    0
    2021-07-31T20:23:48+00:00
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    Answer:

    g(x) = 4(x – 1)(x2 + 4)(x + 6)

    = 4(x – 1)(x + 2)^2(x + 6)

    The roots are:

    1, -2, and -6

    (x – 1), or 1,  has a multiplicity of 4,

    (x + 2), or -2, has a multiplicity of 2,

    and (x + 6), or -6, has a multiplicity of 1

    To determine whether or not they’re real zeros, substitute them into the equation.

    g(1) = 4(1 – 1)2(1 + 2)(1 + 6)

    = 4(0)(3)^2(7)

    = 0(9)(7)

    = 0

    g(-2) = 4(-2 – 1)(-2 + 2)^2(-2 + 6)

    = 4(-3)(0)^2(4)

    = (-12)(0)(4)

    = 0

    g(-6) = 4(-6 – 1)(-6 +2)^2(-6 + 6)

    = 4(-7)(-4)^2(0)

    = (-28)(16)(0)

    = 0

    Since all of the roots, when substituted into the equation equal 0, they’re all real zeros.

    (Sorry for this being so long..I hope it helped!)

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