Question

if the quadratic expression px^2+qx+r has the same sign as that of p ,then find the relation among p,q and r.

Answer 1

Take quadratic equation

$f\left(x\right)=p{x}^2+qx+r$

If p>0, then,

$p{x}^2+qx+r>0$

It is only possible when D<0

$\Rightarrow b^2-4qr<0$

If p<0, then

$p{x}^2+qx+r<0$

so, D<0

$q^2-4pr<0$

So, relation between p,q and r is $q^2-4pr<0$