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For which values of k will x^3-x^2-8x+k=0 have three real roots

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  1. Let f(x)=x^3-x^2-8x=x(x^2-x-8).
    f(x) has 3 real roots.
    f'(x)=3x^2-2x-8=(3x+4)(x-2)
    maxf(x)=f(-4/3)=-64/27-16/9+32/3=176/27
    minf(x)=f(2)=8-4-16=-12

    -176/27<k<12

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