**Important Questions for Class 10 Maths Chapter 2 Polynomials with solutions ** includes all the important topics with detailed explanation that aims to help students to score more marks in Board Exams 2020. Students who are preparing for their Class 10 exams must go through Important Questions for **Class 10 Math Chapter 2 Polynomials**.

## Important Questions for Class 10 Maths Chapter 2 Polynomials

Expert teachers at CBSETuts.com collected and solved 2 Marks and 4 mark important questions for Class 10 Maths Chapter 2 Polynomials. All the solutions given in this page are solved based on CBSE marking scheme and NCERT guidelines.

MathsScienceEnglishSocialHindi AHindi B

**Short Answer Type Questions II [3 Marks]**

**Question 1**

Find the zeroes of the quadratic polynomial 3x^{2} – 2 and verify the relationship between the zeroes and the coefficients.

**Answer:**

**Question 2**

On dividing x^{3} – 8x^{2} + 20x -10 by a polynomial g(x), the quotient and the remainder were x – 4 and 6 respectively. Find g(x).

**Answer:**

**Question 3**

**Answer:**

**Question 4.**

Divide the polynomial x^{4} – 11 x^{2} + 34x – 12 by x – 2 and find the quotient and the remainder. Also verify the division algorithm.

**Answer:**

**Question 5.**

An NGO decided to distribute books and pencils to the students of a school running by some other NGO. For this they collected some amount from different people. The total amount collected is represented by 4x^{4} + 2x^{3} – 8x^{2} + 3x – 7. From this fund each student received an equal amount. The number of students, who received the amount, is represented by x – 2 + 2x^{2}. After distribution, 5x -11, amount is left with the NGO which they donated to school for their infrastructure. Find the amount received by each student from the NGO. What value has been depicted here?

**Answer:**

**Question 6.**

Obtain all other zeroes of the polynomial x^{4} – 17x^{2} – 36x – 20, if two of its zeroes are + 5 and – 2.

**Answer:**

**2015**

**Short Answer Type Questions II [3 Marks]**

**Question 7.**

Divide the polynomial x^{4} – 9x^{2} + 9 by the polynomial x^{2} -3x and verify the division algorithm.

**Answer:**

**Question 8.**

If one zero of the quadratic polynomial f(x) = 4x^{2} – 8kx + 8x – 9 is negative of the other, then find the zeroes of kx^{2} + 3kx + 2.

**Answer:**

**Question 9.**

An NGO decided to distribute books and pencils to the students of a school running by some other NGO. For this, they collected some amount from different number of people. The total amount collected is represented by 4 x^{4} + 2x^{3} – 8x^{2} + 3x – 7. . The amount is equally divided between each of the students. The number of students, who received the amount is represented by x – 2 + 2x^{2}. After distribution, 5x- 11, amount is left with the NGO which they donated to school for their infrastructure. Find the amount received by each student from the NGO.

What value have been depicted here?

**Answer:**

**2014**

**Short Answer Type Questions I [2 Marks]**

**Question 10.**

If the product of zeroes of the polynomial ax^{2} – 6x – 6 is 4, find the value of a. Find the sum of zeroes of the polynomial.

**Answer:**

**Question 11.**

Find the zeroes of the quadratic polynomial 9t^{2}-6t + 1 and verify the relationship between the zeroes and the coefficients.

**Answer:**

**Question 12.**

When a polynomial 6x^{4} + 8x^{3} + 290x^{2} + 21x + 7 is divided by another polynomial 3x^{2} + 4x + 1 the remainder is in the form ax + b. Find a and b.

**Answer:**

**Short Answer Type Questions II [3 Marks]**

**Question 13.**

Obtain all other zeroes of the polynomial x^{4} + 4x^{3}-2x^{2}-20x -15 if two of its zeroes are √5 and -√5

**Answer:**

**Question 14.**

**Answer:**

**Question 15.**

Find the zeroes of the quadratic polynomial 3 x ^{2}– 2 and verify the relationship between the zeroes and the coefficients.

**Answer:**

**Question 16.**

If a polynomial x^{4} – 3x^{3} – 6x^{2} + kx – 16 is exactly divisible by x^{2} – 3x + 2, then find the vaue of A.

**Answer:**

**Question 17.**

Obtain all other zeroes of the polynomial x^{4} – 17x^{2} – 36x – 20, if two of its zeroes are 5 and – 2.

**Answer:**

**Question 18.**

Obtain all other zeroes of the polynomial x^{4} – 3√2x^{3} – 3x^{2} + 3√2x – 4, if two of its zeroes are √2 and 2√2.

**Answer:**

**Question 19.**

Divide the polynomial 3x^{3}– 2x^{2} + 5x – 5 by 3x + 1 and verify the division algorithm.

**Answer:**

**2013**

**Short Answer Type Questions I [2 Marks]**

**Question 20.**

Find a quadratic polynomial whose zeroes are 3 + √2 and 3 – √2.

**Answer:**

**Question 21.**

Find a quadratic polynomial whose zeroes are

**Answer:**

**Question 22.**

Verify whether 2,3 and 1/2 are the zeroes of the polynomial

**Answer:**

**Question 23.**

Obtain all other zeroes of the polynomial x^{4} + 4x^{3} – 2x^{2} – 20x – 15 if two of its zeroes are √5 and -√5.

**Answer:**

**2012**

**Short Answer Type Questions I [2 Marks]**

**Question 24.**

If the zeroes of the polynomial x^{2} + px + q are double in value to the zeroes of 2x^{2} – 5x – 3, find the value of p and q.

**Answer:**

**Question 25.**

Show that 1/2 and -3/2 are the zeroes of the polynomial 4x^{2} + 4x- 3 and verify the relationship between zeroes and coefficients of polynomial.

**Answer:**

Again, all the prime numbers you used to divide above are the Prime Factors of 50.

**Question 26.**

Find the value of b for which (2x + 3) is a factor of 2x^{3} + 9x ^{2}– x-b.

**Answer:**

**Question 27.**

Given that x-√5 is factor of the polynomial x^{3} – 3 -√5 x ^{2}– 5x +15√5, find, all the zeroes of the polynomial.

**Answer:**

**Question 28.**

If the polynomial x^{4} – 6x^{3} + 16x^{2} – 25x + 10 is divided by ( x ^{2}– 2x + k) the remainder comes out to be x+ a, find k and a.

**Answer:**

**Question 29.**

What must be subtracted or added to p(x) = 8 x^{4} + 14x^{3} – 2x^{2} + 8x – 12 so that 4x ^{2} + 3x – 2 is a factor of p(x)?

**Answer:**

**2011**

**Short Answer Type Questions I [2 Marks]**

**Question 30.**

Divide x^{4} – 3x^{2} + 4x + 5 by x^{2 }-x+ 1, find quotient and remainder.

**Answer:**

**Question 31.**

If 2 and -3 are the zeroes of the quadratic polynomial x^{2 }+ (a + 1) x + b; then find the values of a and b.

**Answer:**

**Question 32.**

It being given that 1 is one of the zeroes of the polynomial 7x – x^{3} – 6. Find its other zeroes.

**Answer:**

**Short Answer Type Questions II [3 Marks]**

**Question 33.**

If the polynomial 6x^{4} + 8x^{3} + 17x^{2} + 21x + 7 is divided by another polynomial 3x^{2} + 4x + 1, then what will be the quotient and remainder?

**Answer:**

**Question 34**

On dividing the polynomial 4x^{4} – 5x^{3} – 39x ^{2} – 46x – 2 by the polynomial g(x), the quotient and remainder were x^{2} – 3x – 5 and -5x + 8 respectively. Find g(x).

**Answer:**

**Long Answer Type Questions [4 Marks]**

**Question 35.**

Find other zeroes of the polynomial x ^{4} – 7x^{2} + 12 if it is given that two of its zeroes are √3 and -√3.

**Answer:**

**Question 36.**

Obtain all other zeroes of the polynomial x ^{4}– 3x ^{3}-x ^{2} + 9x – 6, if two of its zeroes are √3 and -√3.

**Answer:**

**Question 37.**

Divide 2x ^{4}– 9x^{3} + 5x ^{2} + 3x – 8 bv x ^{2}– 4x+ 1 and verify the division algorithm.

**Answer:**

**2010**

**Very Short Answer Type Questions [1 Mark]**

**Question 38.**

polynomial.

**Answer:**

**Question 39.**

**Answer:**

**Question 40.**

If one zero of the polynomial x ^{2} – 4x + 1 is 2 + √3, write the other zero

**Answer:**

Short Answer Type Questions I [2 Marks]

**Question 41.**

If two zeroes of the polynomial x ^{3} – 4x ^{2} – 3x + 12 are √3 and -√3, then find its third zero.

**Answer:**

**Question 42.**

If √5 and -√5 are two zeroes of the polynomial x ^{3} + 3 x ^{2} – 5x – 15, find its third zero.

**Answer:**

**Question 43.**

For what value of k, is 3 a zero of the polynomial 2x ^{2} + x + kx

**Answer:**

**Question 44.**

If -1 and 2 are two zeroes of the polynomial 2x ^{3} – x ^{2} – 5x – 2, find its third zero.

**Answer:**

**2009**

**Very Short Answer Type Questions [1 Mark]**

**Question 45.**

For what value of k, (- 4) is a zero of the polynomial x ^{2}-x- (2k + 2)

**Answer:**

**Question 46.**

For what value of p, (-4) is a zero of the polynomial x ^{2} – 2x – (7p + 3)

**Answer:**

**Question 47.**

If 1 is a zero of polynomial p(x) = ax ^{2} – 3 (a – 1) – 1, then find the value of a.

**Answer:**

**Question 48.**

Write the polynomial, the product and sum of whose zeroes are -9/2 and -3/2 respectively.

**Answer:**

**Short Answer type Questions I [2 marks]**

**Question 49.**

If the polynomial 6x ^{4}+ 8x ^{3} + 17x ^{2} + 21x + 7 is divided by another polynomial 3x ^{2} + 4x + 1, the remainder comes out to be (ax + b), find a and b.

**Answer:**

**Question 50.**

If the polynomial x ^{4} + 2x ^{3} + 8x ^{2} + 12x + 18 is divided by another polynomial x ^{2} + 5, the remainder comes out to be px + q, find values of p and q.

**Answer:**

**Question 51.**

Find all the zeroes of the polynomial x ^{3} + 3x ^{2} – 2x – 6, if two of its zeroes are -√2 and √2.

**Answer:**

**Question 52.**

Find all the zeroes of the polynomial 2 x ^{3} +x ^{2} – 6 x – 3, if two of its zeroes are -√3 and √3.

**Answer:**