Class 10 • Maths • Chapter 2
Polynomials
True & False Quiz
Roots. Coefficients. Degree.
✓True
✗False
25
Questions
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Ch.2
Chapter
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X
Class
Why True & False for Polynomials?
How this format sharpens your conceptual clarity
🔵 Polynomials are algebraic expressions powering equations, graphs, and modelling — the language of curves.
✅ T/F tests the relationship between zeroes and coefficients — sum and product of roots — tested every year in CBSE.
🎯 A quadratic has AT MOST 2 zeroes; a cubic AT MOST 3 — the degree defines the maximum, not the actual count.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
Every polynomial of degree 2 is called a quadratic polynomial.
Q 2
The polynomialx \(x^2 + 3x\) is a linear polynomial.
Q 3
The degree of a constant polynomial is 1.
Q 4
The zeros of the polynomialx \(x^2 - 4\) are -2 and 2.
Q 5
The polynomialx \(x^3 + 2x^2 + 5\) has three distinct zeros.
Q 6
If \(k\) is a zero of a polynomialp \(p(x)\), then \(p(k)=0\).
Q 7
\(2x+3\) is a polynomial inxxxof degree 1.
Q 8
The product of zeros of \(x^2 - 5x + 6\).
Q 9
Linear polynomial has at least one zero.
Q 10
The sum of the zeros of \(x^2 - 7x + 10\).
Q 11
The degree of the zero polynomial is 0.
Q 12
\(6x^2 + 4x + 6\) can have real zeros.
Q 13
Every quadratic polynomial can be factored into two linear polynomials.
Q 14
All polynomials are algebraic expressions.
Q 15
The polynomial \(2x^3 \) is cubic.
Q 16
\(x^2 + 1\) has real zeros.
Q 17
The constant term of the polynomial \(3x^2 + 2x + 4\) is 4.
Q 18
A quadratic polynomial has at most two zeros.
Q 19
For \(p(x) = x^2+2x+1\), both zeros are equal.
Q 20
The degree of \(5x^4+2x^3\) is 4.
Q 21
The value of polynomial \(x^2-1\) at \(x=1\) is zero.
Q 22
The degree of a polynomial is always positive.
Q 23
The zeros of \(x^2-1=0\) are only real.
Q 24
If a polynomial is divisible by \(x-2\), then 2 is a zero of the polynomial.
Q 25
\(x^2+3x+7\) can have complex zeros.
Key Takeaways — Polynomials
Core facts for CBSE Boards & exams
1
For quadratic ax²+bx+c: Sum of zeroes = −b/a; Product of zeroes = c/a.
2
For cubic ax³+bx²+cx+d: α+β+γ = −b/a; αβ+βγ+γα = c/a; αβγ = −d/a.
3
A polynomial of degree n has AT MOST n zeroes.
4
Geometrically, zeroes are the x-intercepts of y = p(x).
5
A quadratic with no real zeroes does not cross the x-axis.
6
Division Algorithm: p(x) = g(x)·q(x) + r(x), where deg(r) < deg(g).