Top 20 Polynomials MCQs (CBSE Class 10)
1. The degree of the polynomial x³ – x⁴ + x – 1 is:
Answer: C) 4
The degree is the highest power of the variable (x⁴ here).
2. A polynomial of degree 2 is called:
Answer: B) Quadratic
Degree 2 polynomials are called quadratic (e.g., ax² + bx + c).
3. The zeroes of the polynomial x² – 5x + 6 are:
Answer: B) 2, 3
x² – 5x + 6 = (x-2)(x-3), so zeros are 2 and 3.
4. If one zero of the quadratic polynomial x² + 3x + k is 2, then the value of k is:
Answer: D) -10
Substitute x=2: (2)² + 3(2) + k = 0 ⇒ 4 + 6 + k = 0 ⇒ k = -10.
5. The sum and product of the zeroes of the polynomial 2x² – 8x + 6 are:
Answer: B) Sum = 4, Product = 3
For ax² + bx + c, sum = -b/a = 8/2 = 4, product = c/a = 6/2 = 3.
6. The polynomial whose zeroes are -3 and 4 is:
Answer: B) x² – x – 12
Required polynomial: (x+3)(x-4) = x² – x – 12.
7. If the zeroes of the quadratic polynomial ax² + bx + c are equal, then:
Answer: C) b² – 4ac = 0
Equal roots occur when discriminant D = b² – 4ac = 0.
8. The remainder when x³ – 2x² + x + 1 is divided by (x – 1) is:
Answer: B) 1
By Remainder Theorem, remainder = p(1) = 1 – 2 + 1 + 1 = 1.
9. If (x – 1) is a factor of 2x³ + x² – 4x + k, then the value of k is:
Answer: C) 1
Since (x-1) is factor, p(1)=0 ⇒ 2 + 1 – 4 + k = 0 ⇒ k = 1.
10. The number of zeroes of the polynomial p(x) = x³ – x is:
Answer: C) 3
x³ – x = x(x-1)(x+1) has zeros at x = 0, 1, -1.
11. The graph of a quadratic polynomial is a:
Answer: B) Parabola
All quadratic polynomials graph as parabolas.
12. If α and β are the zeroes of x² – 5x + 6, then α² + β² equals:
Answer: B) 13
α+β=5, αβ=6. α²+β² = (α+β)² – 2αβ = 25 – 12 = 13.
13. A cubic polynomial can have at most ____ zeroes.
Answer: C) 3
The Fundamental Theorem of Algebra states degree = max number of zeros.
14. The zeroes of x² – 3 are:
Answer: B) √3, -√3
x² – 3 = 0 ⇒ x = ±√3.
15. If the product of zeroes of ax² + bx + c is 4, then:
Answer: B) c = 4a
Product of zeros = c/a = 4 ⇒ c = 4a.
16. The polynomial p(x) = x² – 2x + 3 has:
Answer: C) No real zeros
Discriminant D = (-2)² – 4(1)(3) = 4 – 12 = -8 < 0.
17. The sum of the zeroes of 3x² – 5x + 2 is:
Answer: B) 5/3
Sum of zeros = -b/a = -(-5)/3 = 5/3.
18. If one zero of 2x² – px + 6 is 2, the value of p is:
Answer: D) -7
Substitute x=2: 2(4) – p(2) + 6 = 0 ⇒ 8 – 2p + 6 = 0 ⇒ p = 7.
19. The number of polynomials having zeroes as -2 and 5 is:
Answer: C) Infinite
All polynomials k(x+2)(x-5) where k ≠ 0 have these zeros.
20. The graph of y = p(x) is shown below. The number of zeroes of p(x) is:
Answer: C) 3
The graph crosses x-axis at 3 points ⇒ 3 real zeros.