Class 10 Ch-2 Polynomials Worksheet - Goyanka Maths Study - GMS - Learning Simply
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# Class 10 Ch-2 Polynomials Worksheet - Goyanka Maths Study

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

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

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

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

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

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

Question 7
Given that two of the zeroes of the cubic polynomial $a{x}^{3}+b{x}^{2}+cx+d$ are 0, then find the third zero.

Question 8
If the zeroes of the quadratic polynomial ${x}^{2}+\left(a+1\right)x+b$ are 2 and -3, then find the value of a and b.

Question 9
If one of the zeroes of the cubic polynomial ${x}^{3}+a{x}^{2}+bx+c$ is -1, then find the product of the other two zeroes.

Question 10
If a-b, a a+b , are zeroes of ${x}^{3}-6{x}^{2}+8x$, 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 ${x}^{3}-6{x}^{2}+3x+10$ 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\left(x\right)=2{x}^{4}+4{x}^{3}-5{x}^{2}-2x+2$$g\left(x\right)={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 $f\left(x\right)=2{x}^{2}-7x+3$, find the value of ${a}^{2}+{b}^{2}$.

Question 16
Quadratic polynomial $4{x}^{2}+12x+9$ 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 $2{x}^{2}-5x-\left(2k+1\right)$ 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 $f\left(x\right)={x}^{2}-px+q$, then find the values of:
a. ${m}^{2}+{n}^{2}$
b. ${m}^{-1}+{n}^{-1}$

Question 19
If the zeroes of the polynomial $f\left(x\right)={x}^{3}-12{x}^{2}+39x+k$ are in A. P., find the value of k.

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

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