Vidaara.orgClass 10 · Mathematics
CodeVID-M10-02-ZER-01
Zeros of a Polynomial — Assignment
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.
A zero of $p(x)$ satisfies $p(x)=$
- A.$1$
- B.$0$
- C.$x$
- D.$-1$
2.
The degree of a quadratic polynomial is:
- A.$1$
- B.$2$
- C.$3$
- D.$0$
3.
A linear polynomial has at most:
- A.$0$ zeros
- B.$1$ zero
- C.$2$ zeros
- D.$3$ zeros
4.
The zero of $2x-6$ is:
- A.$2$
- B.$3$
- C.$-3$
- D.$6$
5.
A cubic polynomial has at most:
- A.$1$ zero
- B.$2$ zeros
- C.$3$ zeros
- D.$4$ zeros
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Find the zero of $3x-9$.
7.
Find the zeros of $x^2-4$.
8.
How many zeros can $x^3+1$ have at most?
9.
Is $x=1$ a zero of $x^2-1$?
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Find the zeros of $x^2-5x+6$.
11.
Find the zeros of $x^2-9$.
12.
Find the zeros of $6x^2-7x-3$.
13.
Verify that $x=2$ is a zero of $x^2-3x+2$.
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.
If one zero of $x^2-5x+k$ is $2$, find $k$ and the other zero.
Answer Key
Section A — Multiple Choice Questions
- (B) $0$
- (B) $2$
- (B) $1$ zero
- (B) $3$
- (C) $3$ zeros
Section B — Short Answer (2 marks)
- $3$.
- $\pm2$.
- $3$.
- Yes.
Section C — Short Answer (3 marks)
- $2$ and $3$.
- $\pm3$.
- $\tfrac32$ and $-\tfrac13$.
- Yes ($4-6+2=0$).
Section D — Long Answer (5 marks)
- Zeros $4,-2$; sum $2=-b/a$, product $-8=c/a$ (verified).
- $k=6$; other zero $3$.
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