root of the equation x2
+ 8 = 0 is twice the other. Find the roots and all possible values of
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If r and 2r are two the roots, since the sum of the roots of a quadratic function is -b/a, for x2 + kx + 8 = 0 → Sum = 3r = -k/1 = -k so that r = -k/3 → k = -3r.
Also, the product of the roots is c/a, for x2 + kx + 8 = 0 → Product = 2r2 = 8 so that r = ±2. Therefore, the roots are 2 and 4 or -2 and -4, and k = -3r = ±6.