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## Introduction to nature of roots and discriminant (b^2 - 4ac)

If a quadratic equation has:-

2 real and distinct roots, discriminant b^2 - 4ac > 0.

2 equal real roots, discriminant b^2 - 4ac = 0.

no real roots, discriminant b^2 - 4ac < 0.

2 real and distinct roots, discriminant b^2 - 4ac > 0.

2 equal real roots, discriminant b^2 - 4ac = 0.

no real roots, discriminant b^2 - 4ac < 0.

## Solving questions involving nature of roots and discriminant

There are four different types of questions shown in this video and how to solve them.

**First type**: Find the range of values of p for which the equation 4x^2 +12x +15 = p(4x + 7) has two real distinct roots.**Second type**: Find the set of values of m for which the line y = mx - 1 does not intersect the curve y = x^2 - 2x + 3. State also the values of m for which the line is tangent to the curve.**Third type**: Show that the roots of the equation (px - 1)^2 + 3px - 5 = 0 are real and distinct for all real values of p and p ≠ 0.**Fourth type**: Find the range of values of m for which 4x^2 - 2x + 2m - 1 is always positive.