Class 10 Chapter 2- Polynomials

Important Questions for Class 10 Maths Chapter 2 Polynomials With Solutions

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.
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Short Answer Type Questions II [3 Marks]

Question 1
Find the zeroes of the quadratic polynomial 3x² – 2 and verify the relationship between the zeroes and the coefficients.
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Question 2
On dividing x³ – 8x² + 20x -10 by a polynomial g(x), the quotient and the remainder were x – 4 and 6 respectively. Find g(x).
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Question 3

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Question 4.
Divide the polynomial x⁴ – 11 x² + 34x – 12 by x – 2 and find the quotient and the remainder. Also verify the division algorithm.

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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 4x⁴ + 2x³ – 8x² + 3x – 7.  From this fund each student received an equal amount. The number of students, who received the amount, is represented by x – 2 + 2x². 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?
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Question 6.
Obtain all other zeroes of the polynomial x⁴ – 17x² – 36x – 20, if two of its zeroes are + 5 and – 2.
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2015

Short Answer Type Questions II [3 Marks]

Question 7.
Divide the polynomial x⁴ – 9x² + 9 by the polynomial x² -3x and verify the division algorithm.
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Question 8.
If one zero of the quadratic polynomial f(x) = 4x² – 8kx + 8x – 9 is negative of the other, then find the zeroes of kx² + 3kx + 2.
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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 x⁴ + 2x³ – 8x² + 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 + 2x². 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 ax² – 6x – 6 is 4, find the value of a. Find the sum of zeroes of the polynomial.
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Question 11.
Find the zeroes of the quadratic polynomial 9t²-6t + 1 and verify the relationship between the zeroes and the coefficients.
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Question 12.
When a polynomial 6x⁴ + 8x³ + 290x² + 21x + 7 is divided by another polynomial 3x² + 4x + 1 the remainder is in the form ax + b. Find a and b.
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Short Answer Type Questions II [3 Marks]

Question 13.
Obtain all other zeroes of the polynomial x⁴ + 4x³-2x²-20x -15 if two of its zeroes are √5 and -√5
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Question 14.

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Question 15.
Find the zeroes of the quadratic polynomial 3 x ²– 2 and verify the relationship between the zeroes and the coefficients.
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Question 16.
If a polynomial x⁴ – 3x³ – 6x² + kx – 16 is exactly divisible by x² – 3x + 2, then find the vaue of A.
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Question 17.
Obtain all other zeroes of the polynomial x⁴ – 17x² – 36x – 20, if two of its zeroes are 5 and – 2.
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Question 18.
Obtain all other zeroes of the polynomial x⁴ – 3√2x³ – 3x² + 3√2x – 4, if two of its zeroes are √2 and 2√2.
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Question 19.
Divide the polynomial 3x³– 2x² + 5x – 5 by 3x + 1 and verify the division algorithm.
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2013

Short Answer Type Questions I [2 Marks]

Question 20.
Find a quadratic polynomial whose zeroes are 3 + √2 and 3 – √2.
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Question 21.
Find a quadratic polynomial whose zeroes are 
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Question 22.
Verify whether 2,3 and 1/2 are the zeroes of the polynomial
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Question 23.
Obtain all other zeroes of the polynomial x⁴ + 4x³ – 2x² – 20x – 15 if two of its zeroes are √5 and -√5.
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2012

Short Answer Type Questions I [2 Marks]

Question 24.
If the zeroes of the polynomial x² + px + q are double in value to the zeroes of 2x² – 5x – 3, find the value of p and q.
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Question 25.
Show that 1/2 and -3/2 are the zeroes of the polynomial 4x² + 4x- 3 and verify the relationship between zeroes and coefficients of polynomial.
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Question 26.
Find the value of b for which (2x + 3) is a factor of 2x³ + 9x ²– x-b.
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Question 27.
Given that x-√5 is factor of the polynomial x³ – 3 -√5 x ²– 5x +15√5, find, all the zeroes of the polynomial.
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Question 28.
If the polynomial x⁴ – 6x³ + 16x²  – 25x + 10 is divided by ( x ²– 2x + k) the remainder comes out to be x+ a, find k and a.
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Question 29.
What must be subtracted or added to p(x) = 8 x⁴ + 14x³ – 2x² + 8x – 12 so that 4x ² + 3x – 2 is a factor of p(x)?
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2011

Short Answer Type Questions I [2 Marks]

Question 30.
Divide x⁴ – 3x² + 4x + 5 by x² -x+ 1, find quotient and remainder.
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Question 31.
If 2 and -3 are the zeroes of the quadratic polynomial x² + (a + 1) x + b; then find the values of a and b.
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Question 32.
It being given that 1 is one of the zeroes of the polynomial 7x – x³ – 6. Find its other zeroes.
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Short Answer Type Questions II [3 Marks]

Question 33.
If the polynomial 6x⁴ + 8x³ + 17x² + 21x + 7 is divided by another polynomial 3x² + 4x + 1, then what will be the quotient and remainder?
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Question 34
On dividing the polynomial 4x⁴ – 5x³ – 39x ² – 46x – 2 by the polynomial g(x), the quotient and remainder were x² – 3x – 5 and -5x + 8 respectively. Find g(x).
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Long Answer Type Questions [4 Marks]

Question 35.
Find other zeroes of the polynomial x ⁴ – 7x² + 12 if it is given that two of its zeroes are √3 and -√3.
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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.
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Question 37.
Divide 2x ⁴– 9x³ + 5x ² + 3x – 8 bv x ²– 4x+ 1 and verify the division algorithm.
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2010

Very Short Answer Type Questions [1 Mark]

Question 38.
 polynomial.
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Question 39.

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Question 40.
If one zero of the polynomial x ² – 4x + 1 is 2 + √3, write the other zero
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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.
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Question 42.
If √5 and -√5 are two zeroes of the polynomial x ³ + 3 x ² – 5x – 15, find its third zero.
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Question 43.
For what value of k, is 3 a zero of the polynomial 2x ² + x + kx

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Question 44.
If -1 and 2 are two zeroes of the polynomial 2x ³ – x ² – 5x – 2, find its third zero.
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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)
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Question 46.
For what value of p, (-4) is a zero of the polynomial x ² – 2x – (7p + 3)
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Question 47.
If 1 is a zero of polynomial p(x) = ax ² – 3 (a – 1) – 1, then find the value of a.
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Question 48.
Write the polynomial, the product and sum of whose zeroes are -9/2 and -3/2 respectively.
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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.
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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.
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Question 51.
Find all the zeroes of the polynomial x ³ + 3x ² – 2x – 6, if two of its zeroes are -√2 and √2.
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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.