The equation x^{2}-p x+q=0, p, q in R has no | vedclass

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(B) For a quadratic equation $Ax^{2}+Bx+C=0$,the roots are real if the discriminant $D = B^{2}-4AC \geq 0$.
For the equation to have no real roots,th

Vedclass · Accepted Answer

$p^{2} < 4 q$

Vedclass · Answer

(B) For a quadratic equation $Ax^{2}+Bx+C=0$,the roots are real if the discriminant $D = B^{2}-4AC \geq 0$.
For the equation to have no real roots,the discriminant must be less than zero,i.e.,$D < 0$.
Given the equation $x^{2}-px+q=0$,we have $A=1$,$B=-p$,and $C=q$.
Substituting these values into the condition $B^{2}-4AC < 0$:
$(-p)^{2}-4(1)(q) < 0$
$p^{2}-4q < 0$
$p^{2} < 4q$.
Thus,the condition for the equation to have no real roots is $p^{2} < 4q$.

The equation $x^{2}-p x+q=0, p, q \in R$ has no real root if:

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