**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**

*x*2-5*x*+6=0

⇒*x*2-5*x*+6=0

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

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

∴Δ=*b*2-4*ac*

= (-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.