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

We have the quadratic equation \( 2x^2 - 4x - 6 = 0 \). First, divide the entire equation by 2 to simplify: \[ x^2 - 2x - 3 = 0 \] Now, factor the quadratic: \[ x^2 - 2x - 3 = (x - 3)(x + 1) = 0 \] Setting each factor equal to zero: \[ x - 3 = 0 \quad \text{or} \quad x + 1 = 0 \] \[ x = 3 \quad \text{or} \quad x = -1 \] Thus, the roots are \( x = 3 \) and \( x = -1 \), corresponding to option (3).