The quadratic equation has two real roots and

MATHEMATICS · Multi-part · CBSE · Mathematics · Quadratic Equations · Quadratic Equations

Problem

The quadratic equation

x^{2}-(2p+3)x+(p^{2}+p-2)=0

has two real roots

\alpha

and

\beta

, where

p

is a real parameter. (i) Find the range of

p

for which the equation has real roots. (ii) For

p

in this range, determine the value(s) of

p

for which the larger root exceeds the smaller root by

5

. (iii) Hence write the two roots when the condition in part (ii) is satisfied.