 # Class 10 Maths Worksheet for Polynomials

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

Question 1
Find the zeroes of the quadratic polynomial $x^2 + x -12$ and verify the relationship between the zeroes and the coefficients.

Question 2.
Find the quadratic polynomial, the sum and product of whose zeroes are 4 and 1, respectively
Question 3
If a and b are zeroes of the $x^2 + 7x + 7$, find the value of $a^{-1} + b^{-1}-2ab$

Question 4
Find remainder when $x^3 - ax^2 + 6 - a$ is divided by (x - a).

Question 5
If p and q are zeroes of $f(x) = x^2 - 5x + k$, such that $p -q = 1$, find the value of k.

Question 6
Given that two of the zeroes of the cubic polynomial $ax^3 + bx^2 + cx + d$ are 0, then find the third zero.

Question 7
If the zeroes of the quadratic polynomial $x^2 + (a + 1) x + b$ are 2 and -3, then find the value of a and b.

Question 8
If one of the zeroes of the cubic polynomial $x^3 + ax^2+ bx + c$ is -1, then find the product of the other two zeroes.

Question 9
If a-b, a a+b , are zeroes of $x^3-6x^2 + 8x$, then find the value of b

Question 10
If a and b are zeroes of the polynomial $f(x) = 2x^2 - 7x + 3$, find the value of $a^2 + b^2$.

Question 11
Quadratic polynomial $4x^2 + 12x + 9$ has zeroes as p and q . Now form a quadratic polynomial whose zeroes are $p -1$ and $q-1$

Question 12.
Find the remainder when x51 +51 is divided by (x+1).

Question 13
Verify the 1/2 ,1, -2 are zeroes of cubic polynomial $2x^3 + x^2 -5x + 2$. Also verify the relationship between the zeroes and their coefficients.

Question 14
p and q are zeroes of the quadratic polynomial $x^2 - (k + 6)x + 2(2k - 1)$. Find the value of k if $2(p+q) =pq$

Question 15
m, n are zeroes of $ax^2 - 5x + c$. Find the value of a and c if $m + n = m \times n = 10$.

Question 16
Find a quadratic polynomial, the sum and product of whose zeroes are √2 and -3/2 respectively. Also, find its zeroes.

Question 17
Given that the zeroes of the cubic polynomial $x^3 - 6x^2 + 3x + 10$ 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 18
Check whether g(x) is a factor of f(x) by dividing f(x) by g(x):
$f(x) = 2x^4 + 4x^3 - 5x^2 - 2x + 2$, $g(x) = x^2 + 2x- 2$.

Question 19
If one zero of the polynomial $2x^2 - 5x - (2k + 1)$ is twice the other, find both the zeroes of the polynomial and the value of k.

Question 20
If m and n are the zeroes of the quadratic polynomial $f(x) = x^2 - px + q$, then find the values of:
a. $m^2+ n^2$
b. $m^{-1} + n^{-1}$

Question 21
If the zeroes of the polynomial $f(x) =x^3 -12x^2 + 39x + k$ are in A. P., find the value of k.

Question 22
Using division show that $3y^2 + 5$ is a factor of $6y^5+ 15y^4 + 16y^3 + 4y^2 + 10y - 35$.

Question 23.
If the polynomial f(x) = x4 -6x3 + 16x2 - 25x + 10 is divided by another polynomial x2 -2x + k, the remainder comes out to be x + a, find k and a.

Question 24.
Find all the zeroes of the polynomial x4 - 3x3 + 6x - 4, if two of its zeroes are √2  and -√2

Question 25.
If p and q are he zeroes of the quadratic polynomial f(x) = x2 - 2x + 3, find a polynomial whose roots are:
1. p + 2, q + 2
2. (p-1)/(p+1) , (q-1)/(q+1)
Question 26.
For what value of k, -7 is the zero of the polynomial 2x2 + 11x + (6k - 3)? Also find the other zero of the polynomial

Question 27.
What must be added to f(x) = 4x4 + 2x3 - 2x2 + x - 1 so that the resulting polynomial is divisible by g(x) = x2 + 2x -3?

Question 28.
Find k so that x2 + 2x + k is a factor of 2x4 + x3 - 14 x2 + 5x + 6. Also find all the zeroes of the two polynomials.
Question 29.
Find the zeroes of 2x3 - 11x2 + 17x - 6.
Question 30.
If (x - 2) and [x - ½ ] are the factors of the polynomials qx2 + 5x + r prove that q = r

Question 31.
Find k so that the polynomial x2 + 2x + k is a factor of polynomial 2x4 + x3 - 14x2 + 5x + 6. Also, find all the zeroes of the two polynomials.

Question 32.
On dividing p(x) = x3 - 3x2 + x + 2 by a polynomial q(x), the quotient and remainder were x - 2 and -2x + 4, respectively. Find g(x).

Question 33.
a, b, c are zeroes of cubic polynomial x3 - 2x2 + qx - r. If a + b = 0 then show that 2q = r.
Question 34.
a,b and c are zeroes of polynomial x3 + px2 + qx + 2 such that a b + 1 = 0. Find the value of 2p + q + 5.

## Summary

This Class 10 Maths Worksheet for Polynomials with answers is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feedback on the mail. Go back to Class 10 Main Page using below links

### 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