Question

Find the value of $k$ for which the quadratic equation $(3k+1)x^2+2(k+1)x+1=0$, has equal roots. Also find these roots.

Answer 1

Given: The equation has equal roots

$\Rightarrow$ Discriminant $=b^2-4ac=0$

$\Rightarrow$$4{(k+1)}^2-4\times (3k+1)\times 1=0$

$\Rightarrow {(k+1)}^2-(3k+1)=0$

$\Rightarrow k^2+2k+1-3k-1=0$

$\Rightarrow k^2-k=0$

$\Rightarrow k(k-1)=0$

$\therefore k=0,1$