Question

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

kx(x – 2) + 6 = 0

In the following, determine the values of k for which the given quadratic equation has equal roots:

kx(x – 2) + 6 = 0

Answer 1

The given equation is

kx(x - 2) + 6 = 0

⇒ kx² - 2kx + 6 = 0

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

where a = k, b = -2k and c = 6

Therefore, the discriminant

D = b² - 4ac

= (-2k)² - 4 × (k) × (6)

= 4k² - 24k

= 4k(k - 6)

∵ Roots of the given equation are real and equal

∴ D = 0

⇒ 4k(k - 6) = 0

⇒ k = 0

Or

⇒ k - 6 = 0

⇒ k = 6

Hence, the value of k = 0, 6.