Consider the quadratic equation

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

Problem

2t^{2}+(k-3)t+(k+5)=0

, where

k

is a real parameter. (i) Write the expression for the discriminant of the equation. (ii) Determine the set of values of

k

for which the equation has two distinct real roots. (iii) Find the value(s) of

k

for which the equation has equal real roots. (iv) For what values of

k

does the equation have no real roots? Justify your answer.