Finding zeroes of polynomials is an important topic in mathematics. It helps students understand algebra, equations, graphs, and higher-level mathematical concepts. In this article, you will get 100 practice questions on finding the zeroes of linear polynomials. These questions include fractions, decimals, square roots, powers, brackets, negative numbers, and mixed expressions.
These questions are useful for CBSE, State Board, school exams, Olympiads, and foundation preparation.
What Are Zeroes of a Polynomial?
The zero of a polynomial is the value of the variable that makes the polynomial equal to zero.
Example:
p(x) = x + 5
Now,
x + 5 = 0
x = -5
Therefore, -5 is the zero of the polynomial.
How to Find the Zero of a Polynomial?
Step 1: Put the Polynomial Equal to Zero
Example:
p(t) = 3t – 9
3t – 9 = 0
Step 2: Solve the Equation
3t = 9
t = 3
Therefore, 3 is the zero of the polynomial.
Types of Questions Included in This Worksheet
- Simple linear polynomials
- Fraction-based polynomials
- Decimal-based polynomials
- Negative number questions
- Bracket expressions
- Square root questions
- Power and exponent questions
- Mixed algebraic expressions
- Challenge questions
Basic Questions on Finding Zeroes
- p(x) = x + 5
- p(y) = y – 8
- p(t) = 2t + 7
- p(a) = 3a – 9
- p(m) = 5m + 15
- p(z) = 7z – 21
- p(k) = 10k + 40
- p(b) = 4b – 16
- p(r) = 9r + 27
- p(n) = 11n – 44
Questions with Fractions
- p(x) = x/2 + 3
- p(t) = t/3 – 5
- p(y) = 2y/5 + 4
- p(a) = 3a/4 – 6
- p(m) = (m + 1)/2
- p(z) = (z – 7)/5
- p(k) = 5k/6 + 10
- p(b) = 7b/8 – 14
- p(r) = r/9 + 2
- p(n) = 4n/3 – 12
Questions with Decimals
- p(x) = 0.5x + 2
- p(y) = 1.5y – 3
- p(t) = 2.5t + 7.5
- p(a) = 4.2a – 8.4
- p(m) = 0.25m + 5
- p(z) = 3.5z – 10.5
- p(k) = 6.4k + 12.8
- p(b) = 7.5b – 15
- p(r) = 9.9r + 19.8
- p(n) = 1.2n – 4.8
Questions with Negative Numbers
- p(x) = -x + 7
- p(y) = -2y – 8
- p(t) = -3t + 12
- p(a) = -5a – 20
- p(m) = -7m + 35
- p(z) = -9z – 18
- p(k) = -11k + 44
- p(b) = -4b – 16
- p(r) = -6r + 30
- p(n) = -8n – 24
Questions with Brackets
- p(x) = 2(x + 3)
- p(y) = 3(y – 4)
- p(t) = 5(t + 2)
- p(a) = 7(a – 1)
- p(m) = 4(2m + 5)
- p(z) = 6(3z – 9)
- p(k) = 8(k + 7)
- p(b) = 9(b – 11)
- p(r) = 10(5r + 2)
- p(n) = 12(2n – 6)
Questions with Square Roots
- p(x) = x + √4
- p(y) = y – √9
- p(t) = 2t + √16
- p(a) = 3a – √25
- p(m) = m + √49
- p(z) = 5z – √64
- p(k) = 7k + √81
- p(b) = 9b – √100
- p(r) = r/2 + √36
- p(n) = 0.5n – √121
Questions with Powers
- p(x) = x + 2²
- p(y) = y – 3²
- p(t) = 2t + 4²
- p(a) = 5a – 2³
- p(m) = 3m + 5²
- p(z) = 7z – 10²
- p(k) = 8k + 2⁵
- p(b) = 9b – 3³
- p(r) = r/4 + 6²
- p(n) = 0.2n – 2⁴
Mixed Practice Questions
- p(x) = 2x + 5/2
- p(y) = 3y – 9/4
- p(t) = 0.75t + 6
- p(a) = 2a/3 – 8
- p(m) = 5(m – 7)
- p(z) = 7(z + 9)
- p(k) = k + √144
- p(b) = 2b – √169
- p(r) = 4r + 3²
- p(n) = 6n – 5²
Higher Difficulty Questions
- p(x) = (3x + 6)/2
- p(y) = (5y – 15)/3
- p(t) = 0.4t + 2.8
- p(a) = 1.25a – 7.5
- p(m) = -m/5 + 9
- p(z) = -0.8z – 4
- p(k) = 3(k + √25)
- p(b) = 2(b – 2³)
- p(r) = 5r + √196
- p(n) = 7n – 4²
Challenge Questions
- p(x) = (2x + 5)/4 – 3
- p(y) = (3y – 7)/5 + 2
- p(t) = 0.5(t + 8)
- p(a) = 1.5(a – 6)
- p(m) = m + √225 – 5
- p(z) = 2z – 3² + 4
- p(k) = k/2 + 2⁴
- p(b) = 0.25b – √64
- p(r) = -3(r – 9)
- p(n) = 5n/2 + 15
Important Tips to Solve Polynomial Zero Questions
Example:
2x + 6 = 0
2x = -6
x = -3
Simplify Roots and Powers First
Example:
p(y) = y + √49
√49 = 7
So,
y + 7 = 0
y = -7
Convert Decimals into Fractions
If decimals seem difficult, convert them into fractions for easier calculations.
Importance of Finding Zeroes of Polynomials
Finding zeroes is important for:
- Algebra
- Graphs
- Factorization
- Quadratic equations
- Coordinate geometry
- Higher mathematics
This topic is also important for board exams and competitive exams.
Conclusion
These 100 questions on finding zeroes of polynomials are designed for Class 8, 9, and 10 students. The worksheet includes easy, medium, and difficult questions to improve mathematical understanding and problem-solving skills.
Regular practice of these questions will help students solve polynomial problems more confidently and score better in examinations.