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    function

    Given the equation function f(x)=4x^3-kx^2+x+3 , find the value of k such that (2x+1) is a factor
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  2. #2
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    Quote Originally Posted by william View Post
    Given the equation function f(x)=4x^3-kx^2+x+3 , find the value of k such that (2x+1) is a factor
    If 2x + 1 is a factor, then by the factor and remainder theorems...

    f\left(-\frac{1}{2}\right) = 0.

    So we get

    4\left(-\frac{1}{2}\right)^3 - k\left(-\frac{1}{2}\right)^2 - \frac{1}{2} + 3 = 0

    -\frac{1}{2} - \frac{1}{4}k + \frac{5}{2} = 0

    2 = \frac{1}{4}k

    8 = k.
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