Question

Find the value of k for which the following equations has equal roots.$x^2+4kx+(k^2-k+2)=0.$

Answer 1

$x^2+4kx+(k^2-k+2)=0$

For equal roots $D=0$

$D=b^2-4ac$

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

$⟹3k^2+k-2=0$

$⟹3k(k+1)-2(k+1)=0$

$⟹k=-1,k=2/3$

For $k=-1,x^2-4x+4=0$

$⟹(x-2{)}^2=0⟹x=\pm 2$

For $k=2/3,x^2+\left(8/3\right)x+\left(16/9\right)=0$