For the quadratic equation

MATHEMATICS · Multi-part · AoPS · Mathematics · Quadratic Equations - Part 2 · Quadratic Equations - Part 2

Problem

kx^{2}+4x+1=0

(k\neq 0)

, answer the following. (i) Find the set of all real values of

k

for which the equation has two distinct real roots. (ii) Determine the value of

k

for which the equation has equal real roots. (iii) Find the set of all real values of

k

for which the equation has no real roots.