α β equal roots α+β = −b/a αβ = c/a x² − (α+β)x + αβ
p(x)
Chapter 2  ·  Class X Mathematics  ·  MCQ Practice

MCQ Practice Arena

Polynomials

Zeroes, Graphs and Coefficients — Master the Relationship That Scores

📋 50 MCQs ⭐ 28 PYQs ⏱ 55 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
20Easy
22Medium
8Hard
28PYQs
55 secAvg Time/Q
6Topics
Easy 40% Medium 44% Hard 16%

Why Practise These MCQs?

CBSE Class XNTSEState Boards

Polynomials MCQs are among the most direct in Class X — the relationship between zeroes and coefficients appears in both 2-mark and MCQ formats every CBSE year. NTSE algebraic reasoning uses polynomial factorisation. Graph-based zeroes questions (count x-intercepts) are fast, visual marks. Division algorithm MCQs are a CBSE favourite for 3-mark questions.

Topic-wise MCQ Breakdown

Zeroes of a Polynomial (Concept)6 Q
Graphical Meaning of Zeroes8 Q
Sum & Product of Zeroes (Quadratic)14 Q
Sum/Product/Symmetric — Cubic7 Q
Division Algorithm for Polynomials8 Q
Form Polynomial Given Zeroes7 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$\text{Quadratic: } \alpha+\beta = -b/a,\ \alpha\beta = c/a$
$\text{Cubic: } \alpha+\beta+\gamma = -b/a$
$\alpha\beta+\beta\gamma+\gamma\alpha = c/a,\ \alpha\beta\gamma = -d/a$
$p(x) = g(x)\cdot q(x) + r(x)\ (\text{Division Algorithm})$
$\text{Quadratic from zeroes: } x^2-(\alpha+\beta)x+\alpha\beta$

MCQ Solving Strategy

For sum/product MCQs, read the polynomial carefully — make sure it is in standard form ax²+bx+c before applying the formulae. For graph-based zeroes, count how many times the curve crosses the x-axis. For division algorithm MCQs, verify: p(x) = g(x)·q(x) + r(x) and degree of r(x) < degree of g(x). "Form a polynomial" MCQs: write x² − (sum)x + product directly.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Identify zeroes from graph, verify given zeroes by substitution

② Medium

Apply sum/product formulae, find k given a zero

③ Hard

Cubic zero relations, division algorithm with unknown coefficients

★ PYQ

CBSE — find α²+β², form polynomial; NTSE — factorisation reasoning

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 📘✔️ Exercises Step-by-step NCERT solutions ✔️❌ True / False Concept-based True & False ➡ Next Chapter Pair of Linear Equations in Two Variables
🎯 Knowledge Check

Maths — POLYNOMIALS

50 Questions Class 10 MCQs
1
A polynomial of degree 0 is called a ____
2
The degree of the polynomial \(5x^4 - 3x^2 + 2x - 7\) is ____
3
The degree of the zero polynomial is ____
4
The coefficient of \(x^2\) in \(5x^3 + 7x^2 - 4x + 9\) is ____
5
A linear polynomial has degree ____
6
Which of the following is a quadratic polynomial?
7
The zero of the polynomial \(p(x) = x - 3\) is ____
8
The zero of \(p(x) = 2x + 5\) is ____
9
The number of zeros of a cubic polynomial is ____
10
The zeros of the polynomial \(p(x) = x^2 - 1\) are ____
11
The value of \(p(x) = x^2 - 2x + 3\) at \(x = 2\) is ____
12
When \(p(x)\) is divided by \(x - a\), the remainder is \(p(a)\). This is called ____
13
If \(p(x) = x^2 + 2x + 1\), zeros are ____
14
The sum of zeros of \(x^2 - 5x + 6\) is ____
15
The product of zeros of \(2x^2 + 5x + 3\) is ____
16
If zeros of \(x^2 - 7x + 10\) are \(\alpha\) and \(\beta\), then \(\alpha + \beta =\) ____
17
The polynomial whose zeros are 2 and 3 is ____
18
If zeros are equal, the discriminant \(b^2 - 4ac\) is ____
19
If \(x = 1\) is a zero of \(x^3 - 3x^2 + x + 1\), then the remainder is ____
20
Factorise \(x^2 - 16\).
21
Polynomial having zeros at -2 and 5 is ____
22
Zeros of \(x^2 + 9\) are ____
23
If one zero of \(2x^2 + 3x - 5\) is 1, the other is ____
24
A cubic polynomial has maximum how many zeros?
25
The remainder when \(x^3 - 2x^2 + 4x - 8\) is divided by \(x - 2\) is ____
26
\(p(x)\) is divisible by \(x - 3\) if ____
27
Zeros of \(x^2 - 3x + 2\) are ____
28
For \(p(x) = x^2 + 4x + 3\), sum of zeros = ____
29
For \(p(x) = x^2 - 2x + 1\), zeros are ____
30
If a polynomial is divisible by both \(x - 1\) and \(x + 2\), then \(p(1)\) and \(p(-2)\) are ____
31
For \(x^2 - 2kx + (k^2 - 1) = 0\), equal roots are possible when ____
32
If \(p(x)\) divided by \(x - 1\) gives remainder 5, find \(p(1)\).
33
If zeros of \(x^2 + 7x + 10\) are a, ß, find aß.
34
The number of terms in \(3x^2 + 2x - 7\) is ____
35
The degree of \(5y^3 - 4y^5 + 3y\) is ____
36
If \(p(x) = x^2 - 4\), then zeros are ____
37
For \(p(x) = ax^2 + bx + c\), if one zero = 0, then \(c\) = ____
38
The graph of a quadratic polynomial is a ____
39
The graph of a linear polynomial is a ____
40
If the graph of polynomial \(p(x)\) touches x-axis at one point, it has ____
41
The product of zeros of \(3x^2 - 2x - 1\) is ____
42
If zeros of \(x^2 - kx + 9\) are equal, then \(k \)= ____
43
If \(x = 2\) is zero of \(x^3 - 2x^2 + 4x - 8\), quotient polynomial is ____
44
For \(p(x) = 3x^2 - 5x + 2\), sum of zeros = ____
45
A polynomial of degree 3 is called ____
46
If zeros are 1 and -3, the polynomial is ____
47
\(x^2 - 4x + 3 = 0\) has how many zeros?
48
Zeros of \(x^3 - 6x^2 + 11x - 6\) are ____
49
For quadratic \(ax^2 + bx + c\), the relationship between coefficients and zeros is ____
50
If zeros of polynomial are 4 and 5, find polynomial with leading coefficient 2.
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Polynomials Class 10 MCQs (50 Questions) – NCERT with Answers
Polynomials Class 10 MCQs (50 Questions) – NCERT with Answers — Complete Notes & Solutions · academia-aeternum.com
Polynomials Class 10 MCQs with Answers and Explanations (NCERT Based) Master your understanding of Polynomials with these 50 Multiple Choice Questions (MCQs) from NCERT Class 10 Maths Chapter 2. Each question is carefully designed to test key concepts like degree of polynomial, zeros, factor theorem, remainder theorem, and relationships between coefficients and zeros. These MCQs come with answers and detailed explanations, helping you score full marks in CBSE exams, school tests, and…
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    POLYNOMIALS — Learning Resources

    📄 Detailed Notes
    ✔️ True / False
    📌 Exercise
    📝 Exercises
    Polynomials-Exercise 2.1 Polynomials-Exercise 2.2
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    Polynomials Class 10 MCQs (50 Questions) – NCERT with Answers
    Polynomials Class 10 MCQs (50 Questions) – NCERT with Answers — Complete Notes & Solutions · academia-aeternum.com
    Polynomials Class 10 MCQs with Answers and Explanations (NCERT Based) Master your understanding of Polynomials with these 50 Multiple Choice Questions (MCQs) from NCERT Class 10 Maths Chapter 2. Each question is carefully designed to test key concepts like degree of polynomial, zeros, factor theorem, remainder theorem, and relationships between coefficients and zeros. These MCQs come with answers and detailed explanations, helping you score full marks in CBSE exams, school tests, and…
    🎓 Class 10 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
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