Question

Based on the rational root theorem, which of the following are possible roots of P(x) = 12x^10 + 2x^2 – 15?
select all that apply

-2
-5
1
5/2
2/5

Answer 1

By the Rational Root Theorem any rational root p/q (in lowest terms) must have p | 15 and q | 12.

Check each choice:
- -2 = -2/1: numerator 2 does not divide 15 → not possible.
- -5 = -5/1: numerator 5 | 15 and denominator 1 | 12 → possible.
- 1 = 1/1: numerator 1 | 15 and denominator 1 | 12 → possible.
- 5/2: numerator 5 | 15 and denominator 2 | 12 → possible.
- 2/5: numerator 2 does not divide 15 → not possible.

Answer: -5, 1, 5/2.