Study the quadratic equation

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

Problem

(k-2)x^{2}+(2k+3)x+9=0

, where

k

is a real parameter. (i) Determine the set of values of

k

that ensures the equation has two distinct real roots. (ii) For the values of

k

obtained in part (i), show that the product of the roots is less than

4

and hence find all integral values of

k

that satisfy both conditions simultaneously.