Verified answer

EXPLANATION.

Quadratic equation.

⇒ x² - 2(k + 1)x + k² = 0.

As we know that,

For real and equal roots : D = 0.

⇒ D = b² - 4ac.

⇒ [-2(k + 1)²] - 4(1)(k²) = 0.

⇒ 4(k + 1)² - 4k² = 0.

⇒ 4(k² + 1 + 2k) - 4k² = 0.

⇒ 4k² + 4 + 8k - 4k² = 0.

⇒ 8k + 4 = 0.

⇒ 8k = - 4.

⇒ 2k = - 1.

⇒ k = - 1/2.

Value of k = -1/2.

MORE INFORMATION.

Nature of the roots of the quadratic expression.

(1) Roots are real and unequal, if b² - 4ac > 0.

(2) Roots are rational and different, if b² - 4ac is a perfect square.

(3) Roots are real and equal, if b² - 4ac = 0.

(4) If D < 0 Roots are imaginary and unequal Or complex conjugate.

Answer:

k = -1/2

Step-by-step explanation:

For equal roots,

D = 0

where D is discriminant = b^2-4ac

Given quadratic equation is x²-2(k+1)x+k²=0.

so, b = -2(k+1) , a = 1 and c = k^2.

Applying above condition, we get

4(1+k)^2-4(1)(k^2) = 0

4+8k+4k^2-4k^2 = 0

8k = -4

k = -1/2.

So, value of k is -1/2.