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If the roots of p(x) = x^3 - 15x^2 + 74x + c form an arithmetic sequence, find c.

 Oct 28, 2021
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Suppose that the roots are

\(\displaystyle a-d, a, a+d,\)

then the equation will be

\(\displaystyle (x-a+d)(x-a)(x-a-d) \\ =x^{3}-3ax^{2}+(3a^{2}-d)x-a^{3}+ad^{2} =0, \)

so equating coefficients,

\(\displaystyle a = 5,\\ d = 1, \\ c = -120.\)

 Oct 29, 2021

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