Consider the quadratic equation

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

Problem

3x^{2}+kx+12=0

, where

k

is a real parameter. (i) Find the value(s) of

k

for which the equation has real and equal roots. (ii) Find the range of

k

for which the equation has no real roots. (iii) For

k=-10

, state the nature of the roots without solving the equation and give a reason for your answer.