Question

If 3 is a root of the quadratic equation x² - x + k = 0, find the value of p so that the roots of the equation x² +2kx + (k² + 2k + p) = 0 are equal.

Answer 1

It is given that 3 is a root of the quadratic equation x² - x + k = 0

∴ (3)² - 3 + k = 0

⇒ k + 6= 0

⇒ k = - 6

The roots of the equation x² + 2kx + (k² + 2k + p) = 0 are equal.

∴ D = 0

⇒ (2k)² - 4 x 1 x (k² + 2k + p) = 0

⇒ 4k² - 4k² - 8k - 4p = 0

⇒ -8k - 4p = 0

⇒ p = 8k/-4 = - 2k

⇒ p = - 2 x (-6) = 12

Hence, the value of p is 12.