Question

If -5 is a root of the quadratic equation 2x² + px - 15 = 0, and the quadratic equation p(x² + x) + k = 0 has equal roots, find the value of k

Answer 1

It is given that -5 is a root of the quadratic equation 2x² + px - 15 = 0

∴ 2(-5)² + p x (-5) - 15 = 0

⇒ -5p + 35 = 0

⇒ p = 7

The roots of the equation px² + px + k = 0 are equal.

∴ D = 0

⇒ p² - 4pk = 0

⇒ (7)² - 4 x 7 x k = 0

⇒ 49 - 28k = 0

⇒ k = 49/28 = 7/4

Thus, the value of k is 7/4