Answer to Question #349050 in Calculus for Mapula Advice

Question

Which of the following is part of the set of all possible rational zeros of

f(x)=2x4−x3+6x2−5x−8?

Answer 1

Since all coefficients are integers, we can apply the rational zeros theorem.

The trailing coefficient (the coefficient of the constant term) is $-8.$

Find its factors: $\pm1, \pm2, \pm4,\pm8.$

These are the possible values for $p.$

The leading coefficient is $2.$

Find its factors: $\pm1, \pm2.$

These are the possible values for $q.$

Find all possible values of $f/q: \pm\dfrac{1}{1}, \pm\dfrac{1}{2},\pm\dfrac{2}{1},\pm\dfrac{2}{2},\pm\dfrac{4}{1},\pm\dfrac{4}{2},\pm\dfrac{8}{1},\pm\dfrac{8}{2}.$

Simplify and remove the duplicates (if any).

These are the possible rational roots: $\pm1, \pm\dfrac{1}{2}, \pm2, \pm4,\pm8.$