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Vidaara.orgClass 11 · Mathematics
CodeVID-M11-04-QUA-01
Quadratic Equations with Complex Roots — Assignment
Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Equations with Complex Roots
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.
The roots of $x^2+4=0$ are:
  • A.$\pm2$
  • B.$\pm2i$
  • C.$\pm4i$
  • D.$\pm4$
2.
If the discriminant is negative, the roots are:
  • A.real and equal
  • B.complex conjugates
  • C.real and distinct
  • D.both zero
3.
The sum of the roots of $x^2-5x+6=0$ is:
  • A.$6$
  • B.$5$
  • C.$-5$
  • D.$1$
4.
The product of the roots of $x^2+1=0$ is:
  • A.$-1$
  • B.$1$
  • C.$0$
  • D.$i$
5.
$\sqrt{-9}=$
  • A.$3$
  • B.$3i$
  • C.$-3$
  • D.$9i$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Solve $x^2+9=0$.
7.
Find the discriminant of $x^2-2x+5=0$.
8.
Solve $x^2+x+1=0$.
9.
Find the sum and product of the roots of $x^2-3x+4=0$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Solve $x^2-2x+2=0$.
11.
Solve $x^2+4x+5=0$.
12.
Solve $2x^2+x+1=0$.
13.
If one root of $x^2+px+q=0$ (with real $p,q$) is $2+i$, find $p$ and $q$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Solve $x^2+x+1=0$ and verify the sum and product of its roots.
15.
Form a quadratic equation with real coefficients, one of whose roots is $1-2i$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $\pm2i$
  2. (B) complex conjugates
  3. (B) $5$
  4. (B) $1$
  5. (B) $3i$
Section B — Short Answer (2 marks)
  1. $x=\pm3i$.
  2. $-16$.
  3. $x=\dfrac{-1\pm\sqrt3\,i}{2}$.
  4. Sum $3$, product $4$.
Section C — Short Answer (3 marks)
  1. $x=1\pm i$.
  2. $x=-2\pm i$.
  3. $x=\dfrac{-1\pm\sqrt7\,i}{4}$.
  4. $p=-4,\ q=5$.
Section D — Long Answer (5 marks)
  1. Roots $\dfrac{-1\pm\sqrt3\,i}{2}$; sum $=-1$, product $=1$.
  2. $x^2-2x+5=0$.
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