Linear polynomial and its zero Class 10 Maths | Polynomials

Understand it

A linear polynomial has only one zero because its graph is a straight line.
To find the zero, set the expression equal to zero and solve.
For ax+b=0, the zero is x=-b/a.
This chapter uses that simple idea many times in later topics.

Example

For 2x-6, the zero is x=3 because 2(3)-6=0.

Formula and rule

For p(x)=ax+b, a zero is x=-b/a, with a≠0.

A linear polynomial has one zero and its graph is a straight line.

See it worked out

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

Worked example

For p(x)=3x+9, set 3x+9=0.

1Then 3x=-9, so x=-3.
2Therefore the zero is -3.

Method you can reuse

1Write the polynomial equal to zero.
2Move the constant term to the other side.
3Divide by the coefficient of x.
4Check by substitution if time permits.

Visual tip

On a graph, a linear polynomial appears as a straight line cutting the x-axis at one point if the zero is real.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

How many zeros can a linear polynomial have, and how do you find them?

Think first, then show answer

A linear polynomial has exactly one zero. You find it by setting ax+b=0 and solving, which gives x=-b/a when a is not zero.

Common wrong answer

A common wrong answer is x=+b/a.

Why it loses marks: The constant changes sign when shifted to the other side.

Don't mix this up

Students often change the sign wrongly while moving the constant term. They should solve carefully: ax=-b, not ax=b.

Exam tip

For a linear polynomial ax+b, write the zero directly as -b/a after checking that a is not zero.

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

Find the zero of a given linear polynomial, or check whether a stated value is a zero.

1
Enough for 1 mark
A linear polynomial has highest power 1, usually written as ax+b where a is not zero. Its zero is the value of x that makes ax+b equal to 0.
2
Add for 2 marks
Example: For 2x-6, the zero is x=3 because 2(3)-6=0.
3
Add for 3 marks
A linear polynomial has only one zero because its graph is a straight line.

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

Geometrical meaning of zero of a polynomial

A zero of a polynomial is the value of x for which the polynomial becomes 0. On the graph, it is the x-coordinate where the curve touches or cuts the x-axis.

Quadratic polynomial and its zeros

A quadratic polynomial is a polynomial of degree 2, usually written as ax²+bx+c where a is not zero. Its zeros are the values of x that make the polynomial equal to 0.

Verification of given zeros

To verify whether a number is a zero of a polynomial, substitute that number into the polynomial and check whether the value becomes 0.

Cubic polynomial and its zeros

A cubic polynomial is a polynomial of degree 3, usually written as ax³+bx²+cx+d where a is not zero. Its zeros are the values of x that make the polynomial equal to 0.

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Linear polynomial and its zero

Understand it

See it worked out

Check yourself

Write it in the exam

Practice this concept with focused MCQs

Help improve this page

Linear polynomial and its zero

Understand it

See it worked out

Check yourself

Write it in the exam

Related concepts

Practice this concept with focused MCQs

Help improve this page