# Quadratic Equation Class 10 Notes: Chapter 4

Quadratic equations class 10 notes i.e. for chapter 4 provided here can help the class 10 students to prepare this topic in a more effective way and revise the concepts easily. The important points from this chapter which are highlighted here include-

• What is a quadratic equation?
• Roots of a quadratic equation
• Solution of a quadratic equation
• Example questions
• Practice questions
• Articles related to quadratic equations

## What is a Quadratic Equation?

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 $a \neq 0$.

### Roots of a Quadratic Equation

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

For a quadratic equation $ax^{2} + bx + c = 0$, the roots are given by the following formula-

$\frac{-b\pm \sqrt{b^{2}-4ac}}{2a},\, provided,\,b^{2}-4ac\geq 0$

Important Notes:

• Two distinct roots, if $b^{2}-4ac> 0$
• Coincident roots i.e. two equal roots, if $b^{2}-4ac= 0$
• No real roots, if $b^{2}-4ac< 0$

## Solution of a Quadratic Equation

The solution of a quadratic equation is the other term for a root of a quadratic equation. Apart from the quadratic formula mentioned above, the root or the solution of a quadratic equation can be found out by two methods which are-

• The solution of a Quadratic equation by Factorization
• The solution of a Quadratic Equation by Completing the Square Method

### 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.

### Practice Question

1. Find the value of “k” for the equation $2x^{2}+kx+3=0$
2. Is it possible to build a rectangular field of perimeter 80 m and area 400 m2? If so, find its length and breadth.
3. Find the discriminant of the equation $3x^{2}-2x+\frac{1}{3}=0$ and find
the nature of its roots. Find them, if they are real.

### Related Quadratic Equations Articles for Class 10

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#### Practise This Question

If a pool has to be constructed with a boundary of width 14 m consisting of two straight sections 120 m long joining semi-circular ends whose inner radius is 35 m. Then, the area of the boundary is