Quadratic Equations Class 10 Notes Maths Chapter 4

CBSE Class 10 Maths Notes Chapter 4 Quadratic Equations Pdf free download is part of Class 10 Maths Notes for Quick Revision. Here we have given NCERT Class 10 Maths Notes Chapter 4 Quadratic Equations. According to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.

CBSE Class 10 Maths Notes Chapter 4 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.

Quadratic formula: The roots, i.e., α and β of a quadratic equation ax² + bx + c = 0 are given
by $\frac{-b\pm \sqrt{D}}{2a}$ or $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ 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 α and β are the roots of the quadratic equation, then Quadratic equation is x² – (α + β) x + αβ = 0 Or x² – (sum of roots) x + product of roots = 0

where, Sum of roots (α + β) = $\frac{-coefficientofx}{coefficientof{x}^2}=\frac{-b}{a}$

Product of roots (α x β) = $\frac{coefficientterm}{coefficientof{x}^2}=\frac{c}{a}$

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