Question

Choose the correct answer from the given four options :

If the equation {k + 1)x² – 2(k – 1)x + 1 = 0 has equal roots, then the values of k are

Options

•  1, 3

• 0, 3

• 0, 1

• 0, 1

Answer 1

(k + 1)x² – 2(k – 1)x + 1 = 0
Here, a = k + 1, b = -2(k – 1), c = 1
∴ b² – 4ac
= [–2(k –- 1)]² – 4(k + 1)(1)
= 4(k² – 2k + 1) – 4k - 4
= 4k² – 8k + 4 – 4k – 4
= 4k² – 12k
∵ Roots are equal.
∴ b² – 4ac = 0
∴ 4k² – 12k = 0
4k(k – 3) = 0
⇒ 4k(k – 3) = 0
⇒ k(k – 3) = 0
Either k = 0
or
k – 3 = 0,
then k = 3
k = 0, 3.