In polynomial division Degree of remainder is:
- Greater
- Equal
- Less than divisor
- Infinite
Show answer and explanation
Answer: C. Less than divisor
By the division algorithm, deg(remainder) < deg(divisor).
FSC Mathematics: Quadratic Equations, questions with answers
Practise 21 real Federal Board questions on Quadratic Equations from 2023 to 2026. See the answer and explanation as soon as you answer.
21real questions
8multiple choice
5exam sessions
About Quadratic Equations in FSC Mathematics
Quadratic Equations is one of the 14 main chapters in our Federal Board FSC Mathematics question bank (11th class), and about 4% of its real questions come from it. Tayyari Karo has 21 real questions on this chapter from 2023 to 2026; 8 are multiple choice and marked instantly, and the rest are short and long questions with a model answer. By difficulty: 10 medium, 9 easy, 2 hard.
Work through the questions below, then open the explanation for each one. Redo the ones you missed a few days later.
Try 8 real questions
These are real past-paper questions. Think of your answer first, then open the explanation.
If (x−2) is factor of f(x), then f(2)=
- −2
- 0
- 1
- 2
Show answer and explanation
Answer: B. 0
Factor theorem: (x−2) factor ⇒ f(2)=0.
In signal processing, P(x) represents a signal. If P(−1)=0, then the signal has:
- A zero at x=−1
- Unstability
- Periodicity
- Error
Show answer and explanation
Answer: A. A zero at x=−1
P(−1)=0 means x=−1 is a root, i.e. a zero of P.
Remainder of f(x)=x³−2 when divided by (x−1) is:
- −3
- −1
- 1
- 2
Show answer and explanation
Answer: B. −1
f(1)=1−2=−1 (Remainder theorem).
Which one of the following is a factor of x³−6x²+11x−6?
- x+1
- x−1
- x−4
- x+3
Show answer and explanation
Answer: B. x−1
f(1)=1−6+11−6=0 ⇒ (x−1) is a factor.
If the roots of the equation px² + qx + r = 0 are multiplicative inverse of each other then which condition holds?
- p = r
- p = q
- q = r
- pq = r
Show answer and explanation
Answer: A. p = r
Product of roots = r/p. If roots are reciprocals of each other, their product is 1, so r/p = 1 ⇒ p = r.
Find all roots of: f(x)=x³−3x²−4x+12 by Factor theorem.
Show model answer
f(2)=8−12−8+12=0 ⇒ (x−2) is a factor
Synthetic division: depressed equation x²−x−6=0=(x−3)(x+2)
Roots: x = 2, 3, −2
If P(x)=2x³+x²−13x+6, then (a) Verify that (x+3) is a factor of P(x). (b) Factorize P(x) using synthetic division. (c) Find all the roots of P(x). (d) Write complete factorized form of P(x) and confirm by expanding.
Show model answer
(a) P(−3)=2(−27)+9+39+6=−54+9+39+6=0 ⇒ (x+3) is a factor.
(b) Synthetic division of 2,1,−13,6 by −3: → 2,−5,2,0 (remainder 0). Depressed: 2x²−5x+2=0
(c) 2x²−5x+2=0 ⇒ discriminant=25−16=9 ⇒ x=(5±3)/4 = 2 or 1/2
Roots: x = −3, 2, 1/2
(d) P(x) = (x+3)(2x−1)(x−2)
Expand: (x+3)(2x²−5x+2) = 2x³−5x²+2x+6x²−15x+6 = 2x³+x²−13x+6 ✓
Sessions with Quadratic Equations questions
| Session | Questions |
|---|---|
| 2026 Annual | 5 |
| 2025 1st Annual | 5 |
| 2025 2nd Annual | 5 |
| 2024 Annual | 2 |
| 2023 Annual | 4 |
Common questions
What does the Quadratic Equations chapter cover on this page?
21 real Federal Board (FBISE) Mathematics questions on Quadratic Equations from 2023 to 2026, for 11th class. Each one shows the session it came from.
Are the answers official?
No. We could not find an official FBISE marking scheme for these papers, so the answers and explanations are written by Tayyari Karo for practice. Check anything important with your teacher or textbook.
Is it free?
You can start free with no signup. A small set of papers per subject is free, and Premium unlocks the full question bank.
Other Mathematics chapters
- Differentiation 61
- Conic Sections 46
- Vectors 46
- Integration 39
- Functions and Limits 31
- Trigonometric Identities 30
- Matrices and Determinants 29
- Sequences and Series 28
- Introduction to Analytic Geometry 28
- Fundamentals of Trigonometry 26
- Binomial Theorem 20
- Permutation/Combination/Probability 19
- Number Systems 17