Question

Find $m$ so that roots of the equation $(4+m)x^2+(m+1)x+1=0$ may be equal.

Answer 1

Given that the roots of the quadratic equation $(4+m)x^2+(m+1)x+1=0$ are equal.

$\therefore$ the discriminant $b^2-4ac$ will be equal to $0$.

Here $a=4+m,b=m+1,c=1$

$\therefore b^2-4ac=(m+1{)}^2-4(4+m\left)\right(1)=0$

$\Rightarrow (m+1{)}^2-4(4+m)=0$

$\Rightarrow m^2+2m+1-16-4m=0$

$\Rightarrow m^2-2m-15=0$

$\Rightarrow (m-5)(m+3)=0$

$\Rightarrow m=5or-3$