Question

find the value of k if the given equation has equal roots x^2-2(k+1)x+k^2=0​

Answer 1

Answer:

• The value of k is -1/2.

Given:

• The given quadratic equation is
• x²-2(k+1)x+k²=0

To find:

• The value of k if equation has equal roots.

Solution:

The given quadratic equation is x²-2(k+1)x+k²=0

Here, a = 1, b = -2(k+1) and c = k²

If a quadratic equation has equal roots then

D=0

=> b²- 4ac = 0

=> [-2(k+1)]² - 4(1)(k²) = 0

=> 4(k+1)² - 4k² = 0

=> 4(k²+2k+1) - 4k² = 0

=> 4k² + 8k + 4 - 4k² = 0

=> 8k = -4

=> k = -4/8

=> k = -1/2

The value of k is -1/2.