Vidaara.orgClass 10 · Mathematics
CodeVID-M10-04-FAC-01
Factorization & Completing the Square — 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.
The roots of $x^2-5x+6=0$ are:
- A.$2,3$
- B.$1,6$
- C.$-2,-3$
- D.$5,1$
2.
The roots of $x^2-9=0$ are:
- A.$3$
- B.$\pm3$
- C.$9$
- D.$\pm9$
3.
To complete the square of $x^2+8x$, add:
- A.$4$
- B.$8$
- C.$16$
- D.$64$
4.
The roots of $(x-1)(x-4)=0$ are:
- A.$1,4$
- B.$-1,-4$
- C.$2,3$
- D.$1,-4$
5.
The roots of $x^2+2x+1=0$ are:
- A.$1,1$
- B.$-1,-1$
- C.$1,-1$
- D.$0,1$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Solve $x^2-7x+12=0$.
7.
Solve $x^2+5x+6=0$.
8.
Solve $2x^2-8=0$.
9.
Solve $x^2-x-6=0$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Solve $6x^2-x-2=0$ by factorisation.
11.
Solve $x^2+4x-5=0$ by completing the square.
12.
Solve $2x^2+x-6=0$.
13.
Solve $x^2-6x+9=0$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Solve $x^2-4x-8=0$ by completing the square.
15.
Solve $\dfrac{1}{x-1}-\dfrac{1}{x+5}=\dfrac{6}{7}$ ($x\ne1,-5$).
Answer Key
Section A — Multiple Choice Questions
- (A) $2,3$
- (B) $\pm3$
- (C) $16$
- (A) $1,4$
- (B) $-1,-1$
Section B — Short Answer (2 marks)
- $3,\ 4$.
- $-2,\ -3$.
- $\pm2$.
- $3,\ -2$.
Section C — Short Answer (3 marks)
- $\tfrac23,\ -\tfrac12$.
- $1,\ -5$.
- $\tfrac32,\ -2$.
- $3$ (repeated).
Section D — Long Answer (5 marks)
- $x=2\pm2\sqrt3$.
- $x=2$ or $x=-6$.
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