Question

The solution set for the quadratic equation 2x² + kx – k² = 0 is ______.

Options

• {k, k}

• {–k, k}

• `{-k, k/2}`

• `{(-k)/2, k}`

Answer 1

The solution set for the quadratic equation 2x² + kx – k² = 0 is `underlinebb({-k, k/2})`.

Explanation:

⇒ 2x² + kx – k² = 0

⇒ 2x² + 2kx – kx – k² = 0

⇒ 2x(x + k) – k(x + k) = 0

⇒ (2x – k)(x + k) = 0

⇒ 2x – k = 0 or x + k = 0   ...[Using zero-product rule]

⇒ 2x = k or x = –k

⇒ x = `k/2` or x = –k

The solution set: `{-k, k/2}`.