Question

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

Answer 1

+/- 1,
`(+-1)/(+-3),(+-1)/(+-9),+-2,(+-2)/(+-3),(+-2)/(+-9),+-4,(+-4)/(+-3), (+-4)/(+-9)` ....

Explanation:

The Rational root theorem states that If f(x) is a Polynomial with integer coefficients and if there exist a rational root of the form p/q then p is the factor of the constant term of the function and q is the factor of the leading coefficient of the function

Given: f(x)= 9x^4-2x^2-3x+4

Factors of q (leading coefficient) are: +/-9, +/-3, +/-1

Factors of p (constant term) are: +/-4 , +/-2, +/- 1

According to the theorem we write the roots in p/q form:

Therefore,

p/q =+/- 1,
`(+-1)/(+-3),(+-1)/(+-9),+-2,(+-2)/(+-3),(+-2)/(+-9),+-4,(+-4)/(+-3), (+-4)/(+-9)` ....