Use the rational zeros therem to list the potential rational zeros of the polynomial function.

Question

Do not attemt to find the zeros

f(x)= -49x^5-x^4+x+7

Find the potential rational zeros.

Answer 1

f(x)= -49x^5-x^4+x+7

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 7 and q is a factor of 49.

The possible values of p are   ± 1, ± 7.

The possible values for q are ± 1,± 7,± 49.

By the Rational Roots Theorem, the only possible rational roots are, p/q = ± 1,± 7,±1/ 7, and ± 1/49