According to the rational root theorem, what are all the potential rational roots of f(x) = 9x^4 – 2x^2 – 3x + 4?

Step-by-step explanation:

The rational theorem states that if f(x) has integer coefficients and is a rational zero, then q is the factor of leading coefficient and p is the factor of constant term.

Given polynomial=

Now, Factors of leading coefficient q=

factors of constant term p=

according to rational root theorem the rational roots are in the form

: ±1, ± ,  ± , ±2 ±,  ± , ±4,  ±

± .

Step-by-step explanation:

Given: f(x) = .

To find: According to the Rational Root Theorem, what are all the potential rational roots .

Solution: The rational theorem states that if f(x) has integer coefficients and is a rational zero, then q is the factor of leading coefficient and p is the factor of constant term.

                        f(x) = .

Factor of leading coefficient (q) = ±9, ±3, ±1.

Factors of constant term( p)  =  ±4, ±2, ±1.

According to rational root theorem the rational roots are in the form : ±1, ± ,  ± , ±2 ±,  ± , ±4,  ±

± .

Therefore , potential rational roots are : ±1, ± ,  ± , ±2 ±,  ± , ±4,  ±

± .

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