Find the values of k of the following quadratic equation so that they

1.	Find the values of k of the following quadratic equation so that they have two equal roots.kx(x – 2) + 6 = 0
Answer» 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.

Find the values of k of the following quadratic equation so that they have two equal roots.kx(x – 2) + 6 = 0

Answer»

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.