Question

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

$x^2+4xkx+k^2-k+2=0.$

Answer 1

Equation $\to x^2+4kx+k^2-k+2=0$

Equation has equal roots

so, $D=0\Rightarrow b^{2}4ac=0$

$(4k{)}^2-4(k^2-k+2)=0$

$16k^2-4k^2+4k-8=0$

$12k^2+4k-8=0$

Divide the equation by 4.

$3k^2+k-2=0$

$3k^2+3k-2k-2=0$

$3k(k+1)-2(k+1)=0$

$(3k-2)(k+1)=0$

$(3k-2)=0$ and $(k+1)=0$

$k=\frac{2}{3}$ k = -1