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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-02-CT
Polynomials — Full Chapter Test
Chapter: Polynomials
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • This is a full-length test covering the whole chapter — every topic is included.
  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
A zero of $p(x)$ satisfies $p(x)=$
  • A.$1$
  • B.$0$
  • C.$x$
  • D.$-1$
2.
Sum of zeros of $ax^2+bx+c$ is:
  • A.$-\tfrac{b}{a}$
  • B.$\tfrac{c}{a}$
  • C.$\tfrac{b}{a}$
  • D.$-\tfrac{c}{a}$
3.
The degree of a quadratic polynomial is:
  • A.$1$
  • B.$2$
  • C.$3$
  • D.$0$
4.
Product of zeros of $ax^2+bx+c$ is:
  • A.$-\tfrac{b}{a}$
  • B.$\tfrac{c}{a}$
  • C.$\tfrac{b}{a}$
  • D.$a$
5.
A linear polynomial has at most:
  • A.$0$ zeros
  • B.$1$ zero
  • C.$2$ zeros
  • D.$3$ zeros
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the zero of $3x-9$.
7.
Find the sum and product of zeros of $x^2-6x+8$.
8.
Find the zeros of $x^2-4$.
9.
Form a quadratic with zeros $1$ and $-3$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the zeros of $x^2-5x+6$.
11.
If the zeros of $x^2-px+q$ are $2$ and $3$, find $p$ and $q$.
12.
Find the zeros of $x^2-9$.
13.
Form a quadratic whose zeros are $2+\sqrt3$ and $2-\sqrt3$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Find the zeros of $x^2-2x-8$ and verify the relation between zeros and coefficients.
15.
Find the zeros of $6x^2-7x-3$ and verify the relationship between zeros and coefficients.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $0$
  2. (A) $-\tfrac{b}{a}$
  3. (B) $2$
  4. (B) $\tfrac{c}{a}$
  5. (B) $1$ zero
Section B — Short Answer (2 marks)
  1. $3$.
  2. Sum $6$, product $8$.
  3. $\pm2$.
  4. $x^2+2x-3$.
Section C — Short Answer (3 marks)
  1. $2$ and $3$.
  2. $p=5,\ q=6$.
  3. $\pm3$.
  4. $x^2-4x+1$.
Section D — Long Answer (5 marks)
  1. Zeros $4,-2$; sum $2=-b/a$, product $-8=c/a$ (verified).
  2. Zeros $\tfrac32,-\tfrac13$; sum $\tfrac76$, product $-\tfrac12$ (verified).
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