Question

According to the rational zero theorem, which is not possible zero of the function

(x)=2x^4-5x^3+10x^2-9

A. -9
B. -1/2
C. 1/3
D. 3

Answer 1

C. 1/3

Explanation:

You want to identify the rational number listed that cannot be a root of the given polynomial.

Rational root theorem

Possible rational roots will be off the form ...

± (divisor of the constant) / (divisor of the leading coefficient)

Application

When the divisors are listed, this is ...

±{1, 3, 9}/{1, 2}

This shows you that 3 cannot be the denominator of any possible rational root.

1/3 is not a possible zero of the function

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Additional comment

The list of possible roots is ±{1/2, 1, 3/2, 3, 9/2, 9}.

As it happens, neither of the two real roots is rational.

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