 # 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 $2x^3 + x^2 -5x + 2$. Also verify the relationship between the zeroes and their coefficients.

Question 2
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 3
m, n are zeroes of $ax^2 - 5x + c$. Find the value of a and c if $m + n = m \times n = 10$.

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

Question 5
Find remainder when $x^3 - ax^2 + 6 - a$ is divided by (x - a).

Question 6
If p and q are zeroes of $f(x) = x^2 - 5x + k$, such that $p -q = 1$, find the value of k.

Question 7
Given that two of the zeroes of the cubic polynomial $ax^3 + bx^2 + cx + d$ are 0, then find the third zero.

Question 8
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 9
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 10
If a-b, a a+b , are zeroes of $x^3-6x^2 + 8x$, 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 $x^3 - 6x^2 + 3x + 10$ 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 13
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 14
Find the zeroes of the quadratic polynomial $x^2 + x -12$ and verify the relationship between the zeroes and the coefficients.

Question 15
If a and b are zeroes of the polynomial $f(x) = 2x^2 - 7x + 3$, find the value of $a^2 + b^2$.

Question 16
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 17
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 18
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 19
If the zeroes of the polynomial $f(x) =x^3 -12x^2 + 39x + k$ are in A. P., find the value of k.

Question 20
Using division show that $3y^2 + 5$ is a factor of $6y^5+ 15y^4 + 16y^3 + 4y^2 + 10y - 35$.

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.

### 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

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