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

Roots are : -1 or 3

Image attached above

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Given, kx² + 1 - 2(k - 1)x + x² = 0

(k + 1)x² - 2(k - 1)x + 1 = 0

For equal roots D ⇒ b² - 4ac = 0

Here, a = k + 1, b = - 2(k - 1) and c = 1

⇒ 4(k - 1)² - 4(k - 1) × 1 = 0

⇒ 4k² - 8k + 4 - 4k - 4 = 0

⇒ 4k² - 12k = 0

⇒ 4k(k - 3) = 0

⇒ k = 3 or 0

Nature of roots of a quadratic equation:-

(i). If b² - 4ac > 0, the quadratic equation has two distinct real roots.

(ii). If b² - 4ac = 0,  the quadratic equation has two equal real roots.

(iii). If b² - 4ac < 0, the quadratic equation has no real roots.