Question

Rational roots of the equation \( 2x^4 + x^3 - 11x^2 + x + 2 = 0 \) are:

• A. 1/2, 2
• B. 1/3, 2, -2
• C. 1/2, 2, 3, 4
• D. 1/2, 2, 3, -2

Hint:

The Rational Root Theorem states that if a polynomial equation has a rational solution, it must be of the form \( \frac{p}{q} \), where \( p \) is a factor of the constant term and \( q \) is a factor of the leading coefficient.

Answer 1

The Correct Option is A

Step 1: {Apply the Rational Root Theorem}
The Rational Root Theorem dictates that any rational root, represented as \( \frac{p}{q} \), must be a quotient of a factor of the constant term (2) and a factor of the leading coefficient (2).
Step 2: {Identify potential rational roots}
Potential rational roots include \( \pm 1, \pm 2, \pm \frac{1}{2} \). Verification reveals that \( \frac{1}{2} \) and \( 2 \) are the only values that satisfy the equation.