#### Question

Find the value of k for which the following equation has equal roots.

x^{2} + 4kx + (k^{2} – k + 2) = 0

#### Solution

For the given equation x^{2} + 4kx + (k^{2} – k + 2) = 0

a = 1, b = 4k and c = k^{2} - k +1

Since the roots are equal,

b^{2} - 4ac = 0

`=> (4k)^2 - 4xx1xx(k^2 - k + 2) = 0`

`=> 16k^2 - 4k^2 + 4k - `8 = 0`

`=> 12k^2 + 4k - 8 = 0`

`=> 3k^2 + k - 2 = 0`

`=> 3k^2 + 3k - 2k - 2 = 0`

`=> 3k(k+1) - 2(k+1) = 0`

`=> (k+1) (3k - 2) = 0`

`=> k + 1 = 0 or 3k - 2 = 0`

`=> k = -1 or k = 2/3`

Is there an error in this question or solution?

#### APPEARS IN

Solution Find the Value of K for Which the Following Equation Has Equal Roots. X2 + 4kx + (K2 – K + 2) = 0 Concept: Nature of Roots.