List potential rational zeros of the following function.

Question

f(x)= 2x^3 - 11x^2 + 2x + 15.

Answer 1

The function f(x) = 2x³ - 11x² + 2x + 15

Identify Rational Zeros :

Usually it is not practical to test all possible zeros of a polynomial function using only synthetic substitution. The Rational Zero Theorem can be used for finding the some possible zeros to test.

Rational Root Theorem, if a rational number in simplest form p/q is a root of the polynomial equation a_nxⁿ + a_n – 1x^{n – 1} + ... + a₁x + a₀ = 0, then p is a factor of a₀ and q is a factor if a_n.

If p/q is a rational zero, then p  is a factor of 15 and q  is a factor of 2.

The possible values of p  are   ± 1, ± 3, ± 5 and ± 15.

The possible values for q  are ± 1 and ± 2.

By the Rational Roots Theorem,

The only possible rational roots are, p /q = ± 1, ± 3, ± 5, ± 15, ± 1/2, ± 3/2, ± 5/2 and ± 15/2.