# Class 10 Maths Worksheet for Polynomials

Given below are the Class 10 Maths Worksheet for Polynomials
a. cubic polynomials problems
c. Word Problems

Question 1 Verify the  1/2 ,1, -2 are zeroes of cubic polynomial 2x3 + x2 -5 + 2. Also verify the relationship between the zeroes and their coefficients.
Question 2 p and q are zeroes of the quadratic polynomial x2 – (k + 6)x + 2(2k – 1). Find the value of k if 2(p+q) =pq

Question 3 m, n are zeroes of ax2 – 5x + c. Find the value of a and c if m + n = m. n = 10.

Question 4 If  a and b are zeroes of the x2 + 7x + 7, find the value of a-1  + b-1  -2ab

Question 5 Find remainder when x3 – ax2 + 6 – a is divided by (x – a).

Question 6 If  p and q are zeroes of f(x) = x2 – 5x + k, such that  p -q = 1, find the value of k.

Question 7 Given that two of the zeroes of the cubic polynomial ax3 + bx2 + cx + d are 0, then find the third zero.

Question 8 If the zeroes of the quadratic polynomial x2 + (a + 1) x + b are 2 and -3, then find the value of a and b.
Question 9 If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is -1, then find the product of the other two zeroes.
Question 10 If a-b, a a+b ,  are zeroes of x3 -6x2 + 8x, then find the value of b
Question 11 Find a quadratic polynomial, the sum and product of whose zeroes are √2 and -3/2  respectively. Also, find its zeroes.
Question 12 Given that the zeroes of the cubic polynomial x3 – 6x2 + 3x + 10 are of the form a, a + b, a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.

Question 13 Check whether f(x) is a factor of g(x) by dividing f(x) by g(x):
f(x) = 2x4 + 4x3 – 5x2 – 2x + 2, g(x) = x2 + 2x – 2.
Question 14 Find the zeroes of the quadratic polynomial x2 + x -12 and verify the relationship between the zeroes and the coefficients.
Question 15 If a and b are zeroes of the polynomial f(x) = 2x2 – 7x + 3, find the value of a2 + b2.
Question 16 Quadratic polynomial 4x2 + 12x + 9 has zeroes as p and q . Now form a quadratic polynomial whose zeroes are  p -1  and q-1
Question 17 If one zero of the polynomial 2x2 – 5x – (2k + 1) is twice the other, find both the zeroes of the polynomial and the value of k.
Question 18 If   m and n  are the zeroes of the quadratic polynomial f(x) = x2 – px + q, then find the values of:
a. m+ n2
b. m-1 + n-1

Question 19  If the zeroes of the polynomial f(x) = x3 + 39x + k are in A. P., find the value of k.
Question 20 Using division show that 3y2 + 5 is a factor of 6y5 + 15y4 + 16y3 + 4y2 + 10y – 35.

Reference Books for class 10

Given below are the links of some of the reference books for class 10 math.

You can use above books for extra knowledge and practicing different questions.

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### Practice Question

Question 1 What is $1 - \sqrt {3}$ ?
A) Non terminating repeating
B) Non terminating non repeating
C) Terminating
D) None of the above
Question 2 The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is?
A) 19.4 cm3
B) 12 cm3
C) 78.6 cm3
D) 58.2 cm3
Question 3 The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is ?
A) 2 ,21,11
B) 1,10,19
C) -1 ,8,17
D) 2 ,11,20