Question

The equation $x^2-px+q=0p,q\in R$ has no real roots if

• A. $p^2>4q$
• B. $p^2<4q$
• C. $p^2=4q$
• D. None of these

Answer 1

The correct option is B $p^2<4q$

Nature of the roots for a quadratic equation $a^2+bx+c=0$ can be determined by its Discriminant, $D=b^2-4ac$
Here, $D=p^2-4q$
Since, the roots are not real
Therefore,
$D<0$
$=p^2-4q<0$
$=p^2<4q$