CBSE Class 10 Mathematics Chapter 4 - Quadratic Equations - Nature of roots

CBSE Class 10 Mathematics  Chapter 4 - Quadratic Equations - Nature of roots

Nature of Roots:

The general form of quadratic equations is ax² + bx + c = 0, which we can write as quadratic formula

Here, b²—4ac is known as discriminant (D). On the basis of discriminant nature of roots are three types:

• If  b² - 4ac > 0, there are two distinct real roots, given by:

• If  b² - 4ac = 0, there are two equal real roots:

• If  b² - 4ac < 0, there are no real roots for the quadratic equation. In this case, the roots are complex.

Therefore, b² – 4ac determines whether the quadratic equation ax² + bx + c = 0 has real roots or not, b² – 4ac is called the discriminant of this quadratic equation.