Question

Find the discriminant for the following quadratic equation. Also, determine the nature of the roots.

$(x-2p)(x-2q)=4pq;p\ne -q$

• A. D> 0 ; Roots are real and distinct
• B. D=0 ; Roots are real and equal
• C. D < 0 ; Roots are real
• D. D > 0; Roots are not real

Answer 1

The correct option is A D> 0 ; Roots are real and distinct

We have,
$(x-2p)(x-2q)=4pq$
$\Rightarrow x^2-2(p+q)x=0$
Comparing with $a{x}^2+bx+c=0$, we get,
$a=1,b=-2(p+q),c=0$
Discriminant, $D=b^2-4ac=4(p+q{)}^2>0$
$\Rightarrow D>0$
So, the roots are distinct in nature.
Hence, a is the correct option.