Question

Which constant value should be added to the equation $x^2-12x-45=0$ , such that the resulting equation will have 2 equal real roots?

• A. 36
• B. 81
• C. 61
• D. 54

Answer 1

The correct option is B 81

Let 'm' be the constant value.
Then the resulting equation will be $x^2-12x-45+m=0$
Since this equation has 2 equal real roots, its discriminant will be zero.
When you compare $x^2-12x-45+m=0$ to the standard form $a{x}^2+bx+c=0$ we get , a =1,b = (-12) and c = (-45+m)
$\Rightarrow D=b^2-4ac=(-12{)}^2-4\times 1\times (-45+m)=0$
$\Rightarrow 144+(-4\times -45)+(-4\times m)=0$
$\Rightarrow 144+180-4m=0$
$\Rightarrow 4m=324$
$\Rightarrow m=\frac{324}{4}=81$