Question

The roots of quadratic equation \( 2x^2 + x - 4 = 0 \) are:

• A. \( \frac{-1 \pm \sqrt{33}}{4} \)
• B. \( \frac{-1 \pm \sqrt{33}}{2} \)
• C. \( \frac{-1 \pm \sqrt{33}}{2} \)
• D. \( \frac{-1 \pm \sqrt{33}}{4} \)

Hint:

Use the quadratic formula for any quadratic equation of the form \( ax^2 + bx + c = 0 \). Ensure to correctly compute the discriminant \( b^2 - 4ac \).

Answer 1

The Correct Option is A

Apply the quadratic formula. The quadratic formula is: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] For \( 2x^2 + x - 4 = 0 \), we have \( a = 2 \), \( b = 1 \), and \( c = -4 \). Substituting into the quadratic formula: \[ x = \frac{-1 \pm \sqrt{1^2 - 4(2)(-4)}}{2(2)} = \frac{-1 \pm \sqrt{1 + 32}}{4} = \frac{-1 \pm \sqrt{33}}{4} \] Thus, the roots are \( \frac{-1 \pm \sqrt{33}}{4} \).