Page 2 - CHAPTER 4 (Quadratic equations)

CHAPTER 4

QUADRATIC EQUATIONS

A. Introduction

When any polynomial g(x) is written equal to zero then we get an

equation and it is known as a polynomial equation. If g(x) is a linear

polynomial then f(x) = 0 is called a linear equation. An equation is

satisfied by some (finite or infinite) values of a variable.

A polynomial degree 2 is known as a quadratic polynomial. The

general form of a quadratic polynomial is ax + bx + c, where a, b, c ϵ R
2
and a ≠ 0.

Hence, if f(x) is a quadratic polynomial, then f(x) = 0 is called quadratic
equation.

B. Quadratic Equation:

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The standard form of any quadratic equation is: ax + bx + c = 0

Note: Where a, b, c ϵ R and a ≠ 0, if a = 0 then equation will become

linear equation

Any quadratic equation can be of the following types:

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(i) when b = 0, c ≠ 0 i.e. of the type ax + c = 0 (called Pure quadratic
equation)

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(ii) when b ≠0, c = 0 i.e. of the type ax + bx = 0
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(iii) when b, c = 0 i.e. of the type ax =0

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(iv) when b ≠ 0, c≠ 0 i.e. of the type ax + bx + c = 0

Try and learn

Example 1: Check whether the below are quadratic equations or not:

i. (x + 1)² = 2(x – 3) ii. (x – 2) (x + 1) = (x – 1) (x + 3)

iii. (x – 3) (2x + 1) = x (x + 5)

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