Question

Find that non-zero value of k, for which the quadratic equation


kx2 + 1 – 2(k – 1)x + x2 = 0 has equal roots.


Hence, find the roots of the equation.

Answer 1

Given, kx^2 + 1 –2(k – 1)x + x^2 = 0

(k + 1)x^2 – 2(k – 1)x + 1 = 0 1

For equal roots D = b^2 – 4ac = 0

Here, a = k + 1, b = –2(k – 1), c = 1

4(k – 1)^2 – 4(k + 1) × 1 = 0

⇒ 4k^2 – 8k + 4 – 4k – 4 = 0 1

⇒ 4k^2 – 12k = 0

⇒ 4k(k – 3) = 0

k = 0, 3

Since k ≠ 0, k = 3

Answer 2

Equal root means dicriminant =0
Put value of K in equation and solve by shridharacharyas method