Question

find the value of m if the equation has real and equal roots : x2 - (m + 2 ) x + (m + 5) = 0

Answer 1

The Given Equation is  $x^{2} -(m+2)x + (m+5)=0$

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

By using $D=b^2-4ac$

$a=1\\b=(m+2)\\c=(m+5)$

⇒ $(m+2)^2 -4(1*(m+5))$

⇒ $(m^2+4+4m)=4(m+5)$

⇒ $m^2+4+4m=4m+20$

⇒ $m^2+4=20$

⇒ $m^2=20-4$

⇒ $m^2=16$

⇒ $m=4$

Hope it Helps