Question

select the correct answer.

what are the solutions of this quadratic equation?

(2x^2 + 16x - 8 = 0)

(x = 4 pm 2sqrt{5})
(x = -4 pm 2sqrt{5})
(x = 2 pm 4sqrt{5})
(x = -2 pm 4sqrt{5})

Explanation:

Divide the equation by the common factor

$$ x^2 + 8x - 4 = 0 $$

Apply the quadratic formula

$$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-8 \pm \sqrt{8^2 - 4(1)(-4)}}{2(1)} $$

Simplify the radical expression

$$ x = \frac{-8 \pm \sqrt{64 + 16}}{2} = \frac{-8 \pm \sqrt{80}}{2} = \frac{-8 \pm 4\sqrt{5}}{2} = -4 \pm 2\sqrt{5} $$

Answer:

• (A) \(x = 4 \pm 2\sqrt{5}\)
• (B) \(x = -4 \pm 2\sqrt{5}\) (Correct answer)
• (C) \(x = 2 \pm 4\sqrt{5}\)
• (D) \(x = -2 \pm 4\sqrt{5}\)