Question

Find the values of k for the following quadratic equation, so that they have two equal roots.

kx (x - 2) + 6 = 0

Answer 1

kx(x - 2) + 6 = 0

or kx² - 2kx + 6 = 0

Comparing this equation with ax² + bx + c = 0, we get

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

Discriminant = b² - 4ac

= (-2k)² - 4 (k) (6)

= 4k² - 24k

k² - 6k = 0

 k (k - 6) = 0

For equal roots,

b² - 4ac = 0

4k² - 24k = 0

4k (k - 6) = 0

Either 4k = 0 or k = 6 = 0

k = 0 or k = 6

However, if k = 0, then the equation will not have the terms 'x²' and 'x'.

Therefore, if this equation has two equal roots, k should be 6 only.