Discriminant And Nature Of Roots
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.
1. Find the discriminant of Quadratic Equation x2-5x+6=0and discuss the nature of its roots
Comparing the given equation with the standard quadratic equation ax2+bx+c=0,
=25 - 24
Here, Δ>0 and is a perfect square. Also a and b are rational.
Hence, the roots of the equation are distinct and rational.