Rational Again

Algebra Level 3

$x^4-8x^3+14x^2+8x-15 = 0$

If the rational roots of the equation above follows an arithmetic progressions , find their common difference.

The answer is 2.00.

1 solution

Shaun Leong
Dec 30, 2015

It is stated that the roots in A.P. are rational, so we use Rational Root Theorem to see that possible roots are $(\pm 1,\pm 3, \pm 5, \pm 15)$ Trying each root and factoring along the way when we find an actual root, the equation can be factored into $(x-5)(x-3)(x-1)(x+1)$

Hence the roots $-1,1,3,5$ have common difference $\boxed {2}$ .

Rational Again

The answer is 2.00.

1 solution

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