Answer:

Various types of Solved examples on nature of the roots of a quadratic equation:

1. Find the nature of the roots of the equation 3x2 - 10x + 3 = 0 without actually solving them.

Solution:

Here the coefficients are rational.

The discriminant D of the given equation is

D = b2 - 4ac

= (-10)2 - 4 ∙ 3 ∙ 3

= 100 - 36

= 64 > 0.

Clearly, the discriminant of the given quadratic equation is positive and a perfect square.

Therefore, the roots of the given quadratic equation are real, rational and unequal.