Class 9 Polynomials MCQs – Zeroes of a Polynomial & Graphical Interpretation

Class: 9 | Subject: Mathematics | Chapter 2: Polynomials

✔ Based strictly on NCERT (Latest CBSE Syllabus)
✔ Focus on Zeroes of Polynomial & Graphical Interpretation
✔ Ideal for School Exams & CBSE Standard Preparation

1. The zero of the polynomial p(x) = x − 5 is:

A) −5
B) 0
C) 5
D) 1

Correct Answer: C) 5

Explanation: Zero of a polynomial is the value of x for which p(x)=0. x−5=0 ⇒ x=5.

2. Number of zeroes of a linear polynomial is:

A) 0
B) 1
C) 2
D) 3

Correct Answer: B) 1

Explanation: A linear polynomial (degree 1) has exactly one zero.

3. The zeroes of polynomial are graphically represented by:

A) y-intercepts
B) x-intercepts
C) Origin only
D) Quadrants

Correct Answer: B) x-intercepts

Explanation: Zeroes are the points where graph cuts or touches the x-axis.

4. If p(x)=x²−4, then its zeroes are:

A) 2 only
B) −2 only
C) 2 and −2
D) 4 only

Correct Answer: C) 2 and −2

Explanation: x²−4=0 ⇒ (x−2)(x+2)=0 ⇒ x=2, −2.

5. A quadratic polynomial can have at most:

A) 1 zero
B) 2 zeroes
C) 3 zeroes
D) 4 zeroes

Correct Answer: B)

Explanation: Degree 2 ⇒ maximum 2 zeroes.

6. If graph does not cut x-axis, number of zeroes is:

A) 0
B) 1
C) 2
D) 3

Correct Answer: A)

Explanation: No intersection with x-axis ⇒ no real zero.

7. If graph touches x-axis at one point only, number of zeroes is:

A) 0
B) 1
C) 2
D) 3

Correct Answer: B)

Explanation: Touching once means one real zero.

8. Zero of constant non-zero polynomial is:

A) 0
B) 1
C) No zero
D) Infinite

Correct Answer: C)

Explanation: Constant non-zero never equals 0.

9. Zero of p(x)=2x is:

A) 0
B) 2
C) −2
D) 1

Correct Answer: A)

Explanation: 2x=0 ⇒ x=0.

10. Degree of polynomial determines maximum number of:

A) Terms
B) Zeroes
C) Variables
D) Coefficients

Correct Answer: B)

Explanation: Maximum zeroes = degree.

11. If p(1)=0, then 1 is:

A) Factor
B) Zero
C) Coefficient
D) Variable

Correct Answer: B)

Explanation: p(a)=0 ⇒ a is zero.

12. If graph cuts x-axis at 3 points, degree is at least:

A) 1
B) 2
C) 3
D) 4

Correct Answer: C)

Explanation: Minimum degree equals number of zeroes.

13. Polynomial with exactly one zero is:

A) Linear
B) Quadratic
C) Cubic
D) Constant

Correct Answer: A)

Explanation: Linear has one zero.

14. If p(x)=x², its zero is:

A) 0
B) 1
C) −1
D) 2

Correct Answer: A)

Explanation: x²=0 ⇒ x=0.

15. Graph of constant polynomial is:

A) Vertical line
B) Horizontal line
C) Curve
D) Circle

Correct Answer: B)

Explanation: y=c is horizontal line.

16. If graph lies above x-axis completely, number of zeroes is:

A) 0
B) 1
C) 2
D) Infinite

Correct Answer: A)

Explanation: No intersection ⇒ no zero.

17. If p(x)=x²−1, number of zeroes is:

A) 1
B) 2
C) 0
D) 3

Correct Answer: B)

Explanation: x²−1=0 ⇒ x=±1.

18. Zeroes of cubic polynomial can be at most:

A) 1
B) 2
C) 3
D) 4

Correct Answer: C)

Explanation: Degree 3 ⇒ max 3 zeroes.

19. If graph intersects x-axis at origin only, zero is:

A) 0
B) 1
C) −1
D) 2

Correct Answer: A)

Explanation: Origin has x=0.

20. The number of zeroes of a polynomial equals:

A) Degree always
B) Number of x-intercepts
C) Number of terms
D) Number of coefficients

Correct Answer: B)

Explanation: Zeroes are exactly the x-intercepts of graph.

Class 9 Polynomials MCQs – Zeroes of a Polynomial & Graphical Interpretation

Class 9 Polynomials MCQs – Zeroes of a Polynomial & Graphical Interpretation

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