Linear Polynomial in One Variable Class 9 Maths | Introduction to Linear Polynomials

Understand it

In ax + b, a is the coefficient of x and b is the constant term. The zero of the polynomial is the value of x that makes ax + b equal to 0. This is found by solving ax + b = 0.

Example

For p(x) = 2x - 6, the coefficient of x is 2, the constant term is -6, and the zero is x = 3 because 2(3) - 6 = 0.

Formula and rule

General form: ax + b, a ≠ 0.

Zero: ax + b = 0, so x = -b/a.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

Find the zero of 5x + 20.

1Put 5x + 20 = 0.
2Then 5x = -20, so x = -4.
3Check: 5(-4) + 20 = 0.

Method you can reuse

Identify a and b, equate ax + b to 0, isolate x, divide by the coefficient, and substitute the answer back to check.

Visual tip

A number-line mark can show the zero as the value where the polynomial becomes 0.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Find the zero of the linear polynomial p(x) = 3x - 15.

Think first, then show answer

The zero is x = 5 because 3x - 15 = 0 gives 3x = 15, so x = 5.

Common wrong answer

For 2x - 8, students may write x = -4 by using the wrong sign, but 2x - 8 = 0 gives x = 4.

Don't mix this up

Students often ignore the sign of the constant term. In 4x - 12, the constant is -12, not 12.

Exam tip

When finding the zero, write p(x) = 0 first and then solve step by step. Always verify by substitution.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Questions may ask for the coefficient, constant term, degree, zero, or verification of a given zero.

1
Enough for 1 mark
A linear polynomial in one variable is a polynomial of degree 1, usually written as ax + b, where a and b are constants and a is not equal to 0.
2
Add for 2 marks
Example: For p(x) = 2x - 6, the coefficient of x is 2, the constant term is -6, and the zero is x = 3 because 2(3) - 6 = 0.
3
Add for 3 marks
The zero of the polynomial is the value of x that makes ax + b equal to 0.

Use the concept graph around this idea instead of revising it in isolation.

Polynomial — Definition and Degree

A polynomial is an algebraic expression made using variables, constants, coefficients, and non-negative whole number powers of variables. The degree is the highest power of the variable present in the polynomial.

Solving Linear Polynomials

Solving linear polynomials means finding the value or values of variables that make the given linear equation true. At this level, substitution, simple elimination, and verification are useful methods.

Linear Polynomial in Two Variables

A linear polynomial or linear equation in two variables has the form ax + by + c = 0, where x and y are variables, a, b, and c are constants, and a and b are not both zero.

Graphical Visualisation of Linear Polynomials

Graphical visualisation means representing the solutions of a linear equation in two variables as points on the Cartesian plane. These points lie on a straight line.

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Linear Polynomial in One Variable

Understand it

See it worked out

Check yourself

Linear Polynomial in One Variable diagram

Write it in the exam

Practice this concept with focused MCQs

Help improve this page

Linear Polynomial in One Variable

Understand it

See it worked out

Check yourself

Linear Polynomial in One Variable diagram

Write it in the exam

Related concepts

Practice this concept with focused MCQs

Help improve this page