Question

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

kx(x – 2) + 6 = 0

Answer 1

Given: kx(x – 2) + 6 = 0 

kx² – 2kx + 6 = 0 

As this Q.E. has equal roots, 

b² – 4ac = 0 

Here 

a = k; b = -2k; c = 6 

∴ b² – 4ac = (-2k)² – 4(k)(6) = 0

⇒ 4k² – 24k = 0 

⇒ 4k(k – 6) = 0 

⇒ 4k = 0 (or) k – 6 = 0 

⇒ k = 0 (or) 6 

But k = 0 is trivial 

∴ k = 6.