Question

Find all rational roots x^4-7x^2-18=0

Answer 1

To find all the rational roots of the equation x^4 - 7x^2 - 18 = 0, we can apply the Rational Root Theorem. This theorem states that if a polynomial equation has a rational root, then it can be expressed as a fraction of two integers where the numerator divides the constant term and the denominator divides the leading coefficient.

The constant term in this equation is -18, and the leading coefficient is 1. Therefore, the possible rational roots are all the factors of -18 (numerator) divided by the factors of 1 (denominator).

Factors of -18: ±1, ±2, ±3, ±6, ±9, ±18
Factors of 1: ±1

The possible rational roots are:
±1/1, ±2/1, ±3/1, ±6/1, ±9/1, ±18/1

Simplifying, we get:
±1, ±2, ±3, ±6, ±9, ±18

Therefore, the possible rational roots of the equation x^4 - 7x^2 - 18 = 0 are ±1, ±2, ±3, ±6, ±9, and ±18.