Question

Find the discriminant for the quadratic equation represented by $p{x}^2+\sqrt{pq}x+q=0$ and determine the nature of roots. (p and q have same sign)

• A. ${\text{D = 3}}_{pq};\text{Roots are real and equal}$
• B. ${\text{D = -3}}_{pq};\text{Roots are not real}$
• C. ${\text{D = 3}}_{pq};\text{Roots are real and distinct.}$
• D. ${\text{D = -3}}_{pq};\text{Roots are real and equal}$

Answer 1

The correct option is B ${\text{D = -3}}_{pq};\text{Roots are not real}$

$p{x}^2+\sqrt{pq}x+q=0$

$a=p,b=\sqrt{pq},c=q$

$D=b^2-4ac$

$=(\sqrt{pq}{)}^2-4\times p\times q$

$=pq-4pq=-3pq$

Since both p and q have same signs, so D will be negative i.e. <0

$\text{Hence, the roots are not real}.$

$\text{(b) is correct}$