If the ratio of the roots of the equation qx^2+px+q=0 be imaginary ,where p,q>0,then show that 0<p<2q?

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Answer 1 · 2018-02-07T03:08:35

Ratio of the two roots of the given quadratic equation being imaginary then the discriminant must be #<0#

So #p^2-4q^2<0#

#(p+2q)(p-2q)<0#

Given #p>0andq>0#

So #p+2q>0#

Hence #p-2q<0#

#=>p<2q# but given #p>0#

Hence we can say #0 < p <2q#