Discriminant And Nature Of Roots

 

Rules:

1. If D > 0 then the roots are real and distinct. 

(i) If D is a perfect square then the roots are rational and distinct.

(ii) If D is not a perfect square then the roots are irrational and distinct.

2. If D = 0 then the roots are real and equal.

3. If D < 0 then the quadratic equation has no real roots.

Example:

1. Find the discriminant of Quadratic Equation x2-5x+6=0and discuss the nature of its roots

x2-5x+6=0

x2-5x+6=0

Comparing the given equation with the standard quadratic equation ax2+bx+c=0,

we get,a=1,b=-5,c=6.

∴Δ=b2-4ac

= (-5)2-4(1)(6)

=25 - 24

= 1

= (1)2

Here, Δ>0 and is a perfect square. Also a and b are rational.

Hence, the roots of the equation are distinct and rational.