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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-02-REL-01
Zeros & Coefficients — Assignment
Chapter: Polynomials
Topic: Relationship Between Zeros and Coefficients of Quadratic Polynomials
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • 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.
Sum of zeros of $ax^2+bx+c$ is:
  • A.$-\tfrac{b}{a}$
  • B.$\tfrac{c}{a}$
  • C.$\tfrac{b}{a}$
  • D.$-\tfrac{c}{a}$
2.
Product of zeros of $ax^2+bx+c$ is:
  • A.$-\tfrac{b}{a}$
  • B.$\tfrac{c}{a}$
  • C.$\tfrac{b}{a}$
  • D.$a$
3.
For $x^2-7x+10$, the sum of zeros is:
  • A.$10$
  • B.$7$
  • C.$-7$
  • D.$3$
4.
For $x^2-7x+10$, the product of zeros is:
  • A.$7$
  • B.$10$
  • C.$-10$
  • D.$3$
5.
A quadratic with sum of zeros $3$ and product $2$ is:
  • A.$x^2+3x+2$
  • B.$x^2-3x+2$
  • C.$x^2-2x+3$
  • D.$x^2-3x-2$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the sum and product of zeros of $x^2-6x+8$.
7.
Form a quadratic with zeros $1$ and $-3$.
8.
Find the product of zeros of $2x^2-5x+3$.
9.
Find the sum of zeros of $3x^2+6x$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
If the zeros of $x^2-px+q$ are $2$ and $3$, find $p$ and $q$.
11.
Form a quadratic whose zeros are $2+\sqrt3$ and $2-\sqrt3$.
12.
Find a quadratic with sum of zeros $0$ and product $-9$.
13.
If one zero of $x^2+kx+12$ is $3$, find $k$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Find the zeros of $6x^2-7x-3$ and verify the relationship between zeros and coefficients.
15.
Find a quadratic polynomial whose zeros are $5+2\sqrt3$ and $5-2\sqrt3$.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $-\tfrac{b}{a}$
  2. (B) $\tfrac{c}{a}$
  3. (B) $7$
  4. (B) $10$
  5. (B) $x^2-3x+2$
Section B — Short Answer (2 marks)
  1. Sum $6$, product $8$.
  2. $x^2+2x-3$.
  3. $\tfrac32$.
  4. $-2$.
Section C — Short Answer (3 marks)
  1. $p=5,\ q=6$.
  2. $x^2-4x+1$.
  3. $x^2-9$.
  4. $k=-7$.
Section D — Long Answer (5 marks)
  1. Zeros $\tfrac32,-\tfrac13$; sum $\tfrac76$, product $-\tfrac12$ (verified).
  2. $x^2-10x+13$.
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