On this page, you will find Quadratic Equations Class 10 Notes Maths Chapter 4 Pdf free download. CBSE NCERT Class 10 Maths Notes Chapter 4 Quadratic Equations will seemingly help them to revise the important concepts in less time.

## CBSE Class 10 Maths Chapter 4 Notes Quadratic Equations

### Quadratic Equations Class 10 Notes Understanding the Lesson

1. Quadratic Equation: A quadratic equation in the variable x is of the form ax^{2} + bx + c = 0, where a, b, c are real number and a ≠ 0.

2. Roots (or zeroes of a quadratic equation): A real number a is called the root of the quadratic equation

ax^{2} + bx + c = 0 if aα^{2} + bα + c = 0.

Alternatively, any equation of the form p(x) = 0, where p(x) is a quadratic polynomial is a quadratic equation and if p(α) = 0 for any real number a; the a is said to be the root (or zero) of p(x).

Solution of a quadratic equation by factorization

Finding the roots of a quadratic equation by the method of factorization means finding out the linear factors of the quadratic equation and equating it to zero, the roots can be found. i.e. ax^{2} + bx + c = 0

(Ax + B) (Cr + D) = 0

where A, B, C and D are real numbers, A, C≠ 0.

We get Ax + B = 0 or Cx + D = 0

x =\(-\frac{B}{A}\) or x =\(-\frac{D}{C}\)

x =\(-\frac{\mathrm{B}}{\mathrm{A}},-\frac{\mathrm{D}}{\mathrm{C}}\) are the two roots of quadratic equation.

Solution of a quadratic equation by completing the square

For given quadratic equation ax^{2}+ bx + c = 0

Divide the equation by a, so that the coefficient of x^{2} becomes 1.

\(x^{2}+\frac{b}{a} x+\frac{c}{a}=0\)

Adding and subtracting \(\left(\frac{b}{2 a}\right)^{2}\) i.e., square of the half of the coefficient of x.

This formula is known as quadratic formula.

If α and β are roots of the given equation, then

ax^{2} + bx + c = 0,

a ≠ 0, a, b, c ∈ R

Discriminant D = b^{2} – 4ac

Condition exists Nature of roots

(i) b^{2} – 4ac > 0 Real and unequal

(ii) b^{2} – 4ac = 0 Real and equal

(iii) b^{2} – 4ac < 0 No real roots

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