Question

Find the values of k for which the roots are real and equal in each of the following equation:

x² - 4kx + k = 0

Answer 1

The given equation is x² - 4kx + k = 0

The given equation is in the form of ax² + bx + c = 0

where a = 1, b = -4k and c = k

Therefore, the discriminant

D = b² - 4ac

= (-4k)² - 4 x (1) x (k)

= 16k² - 4k

∵ Roots of the given equation are real and equal

∴ D = 0

⇒ 16k² - 4k = 0

⇒ 4k(4k - 1) = 0

⇒ 4k = 0

⇒ k = 0

Or

⇒ 4k - 1 = 0

⇒ 4k = 1

⇒ k = 1/4

Hence, the value of k = 0, 1/4