Question

If the equation $x^2+2(k+2)+9k=0$ has equal roots, find $k$.

Answer 1

The given equation is $x^2+2(k+2)x+9k=0$

For the equation to have equal roots, the discriminant must be equal to zero

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

$\Rightarrow 4(k+2{)}^2-4(9k)=0$

$\Rightarrow (k+2{)}^2=9k$

$\Rightarrow k^2-5k+4=0$

$\Rightarrow k=1,4$