# Quadratic Equations Class 10 Maths Formulas

For those looking for help on Quadratic Equations Class 10 Math Concepts can find all of them here provided in a comprehensive manner. To make it easy for you we have jotted the Class 10 Quadratic Equations Maths Formulae List all at one place. You can find Formulas for all the topics lying within the Quadratic Equations Class 10 Quadratic Equations in detail and get a good grip on them. Revise the entire concepts in a smart way taking help of the Maths Formulas for Class 10 Quadratic Equations.

## Maths Formulas for Class 10 Quadratic Equations

The List of Important Formulas for Class 10 Quadratic Equations is provided on this page. We have everything covered right from basic to advanced concepts in Quadratic Equations. Make the most out of the Maths Formulas for Class 10 prepared by subject experts and take your preparation to the next level. Access the Formula Sheet of Quadratic Equations Class 10 covering numerous concepts and use them to solve your Problems effortlessly.

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