Class 10 Ch-2 Polynomials Worksheet - Goyanka Maths Study

 

Given below are the Class 10 Maths Worksheet for Polynomials
a. cubic polynomials problems
b. quadratic 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 $a{x}^2-5x+c$. 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 $x^3-a{x}^2+6-a$ 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.

Two zeroes = 0, 0
Let the third zero be k.
The, using relation between zeroes and coefficient of polynomial, we have:
$k+0+0=-\frac{b}{a}$
Third zero = k = -b/a

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

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

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 $f\left(x\right)=2x^2-7x+3$, 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 $f\left(x\right)=x^2-px+q$, then find the values of:
a. $m^2+n^2$
b. $m^{-1}+n^{-1}$

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

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