Question

Which of the following is a possible rational zero for the polynomial 6x³ + 9x² - 3x + 2?

	A.	-6
	B.	-3
	C.	0
	D.	2

 

Answer 1

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_nx ⁿ + a_n – 1x ^{n – 1} + ... + a₁x + a₀ = 0, then p is a factor of a₀ and q is a factor if a_n.

The function is 6x³ + 9x² - 3x + 2

If p/q is a rational zero, then p is a factor of 2 and q is a factor of 6.

The possible values of p are   ± 1 and ± 2.

The possible values for q are ± 1 ,± 2 and ± 3

By the Rational Roots Theorem, the only possible rational roots are, p / q = ± 1, ± 2 ,± 2/3 ,± 1/3 and ± 1/2.

Therefore, the Rational zeros are ± 1, ± 2 ,± 2/3 ,± 1/3 and ± 1/2.

The option D is correct.