# Quadratic Equation For Class 10

A polynomial having the degree of 2 is said to be a Quadratic equation. The general representation of quadratic equation is given as $ax^{2} + bx + c = 0$, where $a \neq 0$.

A quadratic equation is suppose to have two roots (say $\alpha$ and $\beta$) that will satisfy the equation and result in the value of $p(\alpha) = p(\beta) = 0$

Solution of Quadratic equation by Factorization-

Solution of Quadratic Equation by Completing the square method-

Consider the Expression $x^{2} + 4x$.

Let us understand the method of completing the square pictorially.

The process is as follows-

$x^{2} + 4x = \left ( x^{2} +\frac{4}{2}x \right ) + \frac{4}{2}x$

$= x^{2} + 2x + 2x$

$= (x+2)x + 2 \times x$

$= (x+2)x + 2 \times x + 2 \times 2 – 2 \times 2$

$= (x+2) \times (x+2) – 2 \times 2$

$= (x+2)^{2} – 4$<

This method is known as the method of completing the square.

#### Practise This Question

The window shown in the shape of a semi-circle with radius 4 ft. The distance from S to T is 2 ft and the measure of ˆAB=45. Area of glass in the region ABCD is