Value and zeroes of a polynomial: Class 9 practice

What you should know first

• Integers
• Simple equations

The idea behind value and zeroes of a polynomial

p(a) means substitute x = a. A zero of p(x) is a value of x that makes p(x) = 0. A linear polynomial ax + b has one zero, x = −b/a.

Step-by-step method

1. Substitute the value for x.
2. Evaluate carefully with signs.
3. For zeroes, solve p(x) = 0.

Worked example 1 (Basic)

Find p(2) for p(x) = 2x² + 1x − 5.

1. 2(2)² + 1(2) − 5
2. = 5
3. Answer: 5

Worked example 2 (Standard)

Find the zero of p(x) = 6x + 54.

1. 6x + 54 = 0
2. x = -9
3. Answer: -9

Worked example 3 (Challenge)

Check whether 3 and -1 are zeroes of x² − 2x − 3.

1. p(3) = 0
2. p(-1) = 0
3. Answer: Both are zeroes

Common mistakes and misconceptions

• Sign errors with negative values
• Confusing p(0) with the zero

Practice questions

1. (Basic) Find p(3) for p(x) = 5x² − 9x + 8.
2. (Basic) Find p(-1) for p(x) = 3x² − 5x − 1.
3. (Standard) Find the zero of p(x) = 4x + 4.
4. (Standard) Find the zero of p(x) = 4x − 24.
5. (Challenge) Check whether -2 and 0 are zeroes of x² + 2x + 0.
6. (Challenge) Check whether -5 and 4 are zeroes of x² + 1x − 20.

Answer key with full working

• Q1: 5(3)² − 9(3) + 8 → = 26 → Answer: 26
• Q2: 3(-1)² − 5(-1) − 1 → = 7 → Answer: 7
• Q3: 4x + 4 = 0 → x = -1 → Answer: -1
• Q4: 4x − 24 = 0 → x = 6 → Answer: 6
• Q5: p(-2) = 0 → p(0) = 0 → Answer: Both are zeroes
• Q6: p(-5) = 0 → p(4) = 0 → Answer: Both are zeroes

Syllabus note

This skill is listed under "Polynomials" for Class 9 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

Related practice and notes

• Polynomials chapter notes (Class 9)
• Remainder theorem and factor theorem
• Factorising by splitting the middle term
• Cube identities
• Area of a triangle by Heron's formula
• Rationalising the denominator
• Recurring decimals to fractions
• Simplifying surds
• All Class 9 practice

Frequently asked questions

Which chapter is value and zeroes of a polynomial in?

"Polynomials", Class 9 Maths (NCERT/CBSE). Other boards may place it differently.

How were the answers checked?

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.