Possible Rational Roots III

Problem 263: Given the polynomial

$y = x^2 + 5x - 14$

list the possible rational roots.

Solution: To find the possible roots of this polynomial we have to consider the possible factors of leading coefficient (call it $q$ ) and the constant coefficient (call it $p$ ).

That is, the possible factors of 1 are: $\pm 1$ .

The possible factors of -14 are: $\pm 1, \pm 2, \pm 7, \pm 14$ .

The possible roots are given by

$\frac{p}{q} = \frac{-1, 1, 2, -2, 7, -7, 14, -14}{-1,1} = \frac{\pm 1, \pm 2 , \pm 7, \pm 14}{\pm 1}.$

Simplifying, the possible roots are

$\frac{p}{q} = \pm 1, \pm 2, \pm 7, \pm 14.$

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