Given below are the Class 10 Maths Worksheet for Polynomials

a. cubic polynomials problems

b. quadratic polynomials Problems

c. Word Problems

a. cubic polynomials problems

b. quadratic polynomials Problems

c. Word Problems

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.

Solution

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

Solution

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

Solution

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

Solution

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

Solution

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

Solution

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

Solution

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.

Solution

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.

Solution

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

Solution

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

Solution

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.

Solution

Check whether g(x) is a factor of f(x) by dividing f(x) by g(x):

$f(x) = 2x^4 + 4x^3 - 5x^2 - 2x + 2$, $g(x) = x^2 + 2x- 2$.

Solution

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

Solution

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

Solution

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

Solution

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.

Solution

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. $m^{-1} + n^{-1}$

Solution

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

Solution

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

Solution

**Notes****NCERT Solutions****Assignments**

Class 10 Maths Class 10 Science