Question

Without solving the following quadratic equation, find the value of $m$ for which the given equation has real and equal roots.
$x^2+2(m-1)x+(m+5)=0$

Answer 1

The given equation is $x^2+2(m-1)x+(m+5)=0$

For the equation to have real and equal roots, the discriminant should be $0$.

$\therefore \left[2\right(m-1){]}^2-4(m+5)=0$
$\Rightarrow 4(m^2-2m+1)=4(m+5)$

$\Rightarrow m^2-3m-4=0$

$\Rightarrow (m-4)(m+1)=0$

$\therefore m=4$ or $m=-1$