Class 10 Maths Polynomials Worksheet — Free Printable PDF
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⭐ MeritMate — Class 10 Maths: Polynomials
Curriculum-Aware · meritmate.inSection A: Multiple Choice Questions
Q1. If the zeroes of the quadratic polynomial x² + (a+1)x + b are 2 and -3, then the values of a and b are:
a) a = -7, b = -1
b) a = 5, b = -1
c) a = 2, b = -6
d) a = 0, b = -6
Q2. The number of zeroes a cubic polynomial can have at most is:
a) 1
b) 2
c) 3
d) 4
Q3. If one zero of the polynomial 3x² - 8x + k is the reciprocal of the other, then the value of k is:
a) 1
b) 2
c) 3
d) 4
Q4. The graph of y = p(x) is given below. The number of zeroes of p(x) is 3. Which of the following graphs represents a polynomial with exactly 3 zeroes?
a) A graph that touches the x-axis at 3 points without crossing
b) A graph that crosses the x-axis at exactly 3 distinct points
c) A graph that lies entirely above the x-axis
d) A graph that crosses the x-axis at only 1 point
Q5. If p(x) = x² - 5x + 6, then the zeroes of p(x) are:
a) 2 and 4
b) -2 and -3
c) 2 and 3
d) -2 and 3
Section B: Fill in the Blanks
Q6. A polynomial of degree 2 is called a ________.
Q7. If the product of zeroes of the polynomial ax² - 6x - 6 is 4, then the value of a is ________.
Q8. The sum of zeroes of the polynomial p(x) = 7x² - 5x + 2 is ________.
Q9. A quadratic polynomial whose zeroes are 5 and -3 is ________.
Q10. The zero of the linear polynomial p(x) = 3x - 9 is ________.
Section C: Short Answer Questions
Q11. Find the zeroes of the quadratic polynomial p(x) = x² - 3x - 10 and verify the relationship between the zeroes and the coefficients.
Q12. If the sum of the zeroes of the quadratic polynomial f(x) = kx² + 2x + 3k is equal to their product, find the value of k.
Q13. Divide the polynomial p(x) = x³ - 3x² + 5x - 3 by g(x) = x² - 2 and find the quotient and remainder.
Q14. If alpha and beta are the zeroes of the polynomial x² - 5x + 6, find the value of (1/alpha) + (1/beta).
Q15. On dividing x³ - 3x² + x + 2 by a polynomial g(x), the quotient and remainder were (x - 2) and (-2x + 4) respectively. Find g(x).
⭐ Answer Key
Class 10 · Maths · PolynomialsAnswer Key
Q1. Answer: d) a = 0, b = -6
Explanation: Sum of zeroes = 2 + (-3) = -1 = -(a+1)/1, so a+1 = 1, giving a = 0. Product of zeroes = 2 x (-3) = -6 = b. So a = 0, b = -6.
Q2. Answer: c) 3
Explanation: A polynomial of degree n can have at most n zeroes. A cubic polynomial has degree 3, so it can have at most 3 zeroes.
Q3. Answer: c) 3
Explanation: If one zero is alpha, the other is 1/alpha. Product of zeroes = alpha x (1/alpha) = 1 = k/3. Therefore k = 3.
Q4. Answer: b) A graph that crosses the x-axis at exactly 3 distinct points
Explanation: The number of zeroes of a polynomial equals the number of points where the graph crosses or touches the x-axis. Exactly 3 crossing points means exactly 3 zeroes.
Q5. Answer: c) 2 and 3
Explanation: Factorising x² - 5x + 6 = (x - 2)(x - 3). Setting each factor to zero gives x = 2 and x = 3.
Q6. Answer: quadratic polynomial
Q7. Answer: -3/2
Explanation: Product of zeroes = -6/a = 4, so a = -6/4 = -3/2.
Q8. Answer: 5/7
Explanation: Sum of zeroes = -coefficient of x / coefficient of x² = -(-5)/7 = 5/7.
Q9. Answer: x² - 2x - 15
Explanation: Sum of zeroes = 5 + (-3) = 2. Product of zeroes = 5 x (-3) = -15. Polynomial = x² - (sum)x + product = x² - 2x - 15.
Q10. Answer: 3
Explanation: Setting 3x - 9 = 0 gives 3x = 9, so x = 3.
Q11. Answer:
Factorising x² - 3x - 10 = (x - 5)(x + 2). Zeroes are x = 5 and x = -2.
Verification:
Sum of zeroes = 5 + (-2) = 3 = -(-3)/1 = 3. This matches -b/a.
Product of zeroes = 5 x (-2) = -10 = -10/1. This matches c/a.
The relationship is verified.
Q12. Answer:
Sum of zeroes = -2/k. Product of zeroes = 3k/k = 3.
Given that sum = product:
-2/k = 3
k = -2/3.
Q13. Answer:
Dividing x³ - 3x² + 5x - 3 by x² - 2:
x³ - 3x² +
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