Question

Find the roots of the quadratic equation \( 2x^2 - 4x - 6 = 0 \).

• A. \( x = 1, -3 \)
• B. \( x = -3, 1 \)
• C. \( x = 3, -1 \)
• D. \( x = -1, 3 \)

Hint:

To solve a quadratic equation, try factoring first. If factoring isn't easy, use the quadratic formula.

Answer 1

The Correct Option is C

Given the quadratic equation \( 2x^2 - 4x - 6 = 0 \), simplify by dividing by 2: \[ x^2 - 2x - 3 = 0 \] Factor the simplified quadratic: \[ x^2 - 2x - 3 = (x - 3)(x + 1) = 0 \] Equate each factor to zero: \[ x - 3 = 0 \quad \text{or} \quad x + 1 = 0 \] Solve for x: \[ x = 3 \quad \text{or} \quad x = -1 \] The roots are \( x = 3 \) and \( x = -1 \), which matches option (3).