NCERT Notes for Class 10 Maths Chapter 4 Quadratic Equations

Class 10 Maths Chapter 4 Quadratic Equations Notes

 Chapter Name Quadratic Equations Notes Class CBSE Class 10 Textbook Name NCERT Mathematics Class 10 Related Readings Notes for Class 10Notes for Class 10 MathsRevision Notes for Quadratic Equations

A quadratic polynomial of the form ax² + bx + c, where a ≠ 0 and a, b, c are real numbers, is called a quadratic equation
when ax² + bx + c = 0.
Here, a and b are the coefficients of x² and x respectively and ‘c’ is a constant term.

Any value is a solution of a quadratic equation if and only if it satisfies the quadratic equation.

The roots, i.e., Î± and Î² of a quadratic equation ax² + bx + c = 0 are given by

provided b² – 4ac ≥ 0.

Here, the value b² – 4ac is known as the discriminant and is generally denoted by D. ‘D’ helps us to determine the nature of roots for a given quadratic equation. Thus, D = b² – 4ac.

The rules are:

1. If D = 0 ⇒ The roots are Real and Equal.
2. If D > 0 ⇒ The two roots are Real and Unequal.
3. If D < 0 ⇒ No Real roots exist.

If Î± and Î² are the roots of the quadratic equation, then Quadratic equation is x² – (Î± + Î²) × + Î±Î² = 0 Or x² – (sum of roots) x + product of roots = 0