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: {Use Rational Root Theorem}
The rational root theorem states that any rational root, say \( \frac{p}{q} \), must be a factor of the constant term (2) divided by a factor of the leading coefficient (2).
Step 2: {Find possible rational roots}
Possible rational roots: \( \pm 1, \pm 2, \pm \frac{1}{2} \). Testing these values, we find that only \( \frac{1}{2} \) and \( 2 \) satisfy the equation.