Consider the quadratic equation where are real numbers and

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

Problem

Consider the quadratic equation

ax^2+bx+c=0

where

a, b, c

are real numbers and

a\neq 0

. Answer the following: (i) Write the expression for the discriminant

D

of the equation and describe how the sign of

D

determines the nature of the roots. (ii) For the equation

5x^2-4x+1=0

, calculate the discriminant and comment on the nature of its roots. (iii) Find the smallest real value of

m

such that the equation

5x^2-4x+m=0

possesses two real and equal roots.