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10 August, 22:49

Approximate the real zeros of f (x) = 2x^4 - x^3 + x-2 to the nearest tenth

a - 1,1

c. 0,1

b. - 2. - 1

d - 1,0

+2
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  1. 11 August, 02:17
    0
    -1.0, 1.0

    Step-by-step explanation:

    The given polynomial function is

    f (x) = 2 {x}^{4} - {x}^{3} + x - 2

    According to the Rational Roots Theorem, the possible roots of this function are;

    /pm1,/pm / frac{1}{2}

    We now use the Remainder Theorem to obtain;

    f (1) = 2 { (1) }^{4} - { (1) }^{3} + 1 - 2

    f (1) = 2 - 1 + 1 - 2 = 0

    f ( - 1) = 2 { ( - 1) }^{4} - { ( - 1) }^{3} - 1 - 2

    f ( - 1) = 2 + 1 - 1 - 2 = 0

    But;

    f (/frac{1}{2}) = - 1.5

    f ( - / frac{1}{2}) = - 2.25

    Since f (1) = 0 and f (-1) = 0, the real zeros to the nearest tenth are:

    -1.0 and 1.0
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