Share

# Find the Values of K for Which the Following Equation Have Real and Equal Root: - Mathematics

Course

#### Question

Find the value of k for which the following equations have real and equal roots:

$x^2 - 2\left( k + 1 \right)x + k^2 = 0$

#### Solution

The given quadric equation is x^2 - 2 (k + 1)x +k^2 = 0, and roots are real and equal

Then find the value of k.

Here,

a = 1, b=2(k + 1)and,c = k2

As we know that D = b^2 - 4ac

Putting the value of  a = 1,b = -2(k+1)and, c = k2

={-2(k+1)}^2 - 4 xx 1 xx k^2

={4(k^2 + 2k +1)} - 4k^2

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

= 8k + 4

The given equation will have real and equal roots, if D = 0

8k + 4 = 0

8k = - 4

k=(-4)/8

 = (-1)/2

Therefore, the value of k = (-1)/2

Is there an error in this question or solution?