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 \(p(\alpha) = p(\beta) = 0\)

**Quadratic Formula**

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

\(\frac{-b\pm \sqrt{b^{2}-4ac}}{2a},\, provided,\,b^{2}-4ac\geq 0\)This method is called **solving quadratic equation using the quadratic formula.**

**Important Notes:**

A quadratic equation will have:

- 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 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**.

### Practice Question

- Find the value of “k” for the equation \(2x^{2}+kx+3=0\)
- Is it possible to build a rectangular field of perimeter 80 m and area 400 m2? If so, find its length and breadth.
- 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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