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# R.S. Aggarwal solutions for Class 10 Mathematics chapter 2 - Polynomials

## Chapter 2: Polynomials

#### Chapter 2: Polynomials solutions [Page 0]

Find the zeros of the polynomial f(x) = x^2 + 7x + 12 and verify the relation between its zeroes and coefficients.

Find the zeroes of the polynomial f(x) = x^2 ˗ 2x ˗ 8 and verify the relation between its zeroes and coefficients

Find the zeroes of the quadratic polynomial f(x) = x^2 + 3x ˗ 10 and verify the relation between its zeroes and coefficients.

Find the zeroes of the quadratic polynomial f(x) = 4x^2 ˗ 4x ˗ 3 and verify the relation between its zeroes and coefficients.

Find the zeroes of the quadratic polynomial f(x) = 5x^2 ˗ 4 ˗ 8x and verify the relationship between the zeroes and coefficients of the given polynomial.

Find the zeroes of the polynomial f(x) = 2sqrt3x^2-5x+sqrt3 and verify the relation between its zeroes and coefficients.

Find the zeroes of the quadratic polynomial 2x^2 ˗ 11x + 15 and verify the relation between the zeroes and the coefficients.

Find the zeroes of the quadratic polynomial 4x^2 ˗ 4x + 1 and verify the relation between the zeroes and the coefficients.

Find the zeroes of the quadratic polynomial (x^2 ˗ 5) and verify the relation between the zeroes and the coefficients.

Find the zeroes of the quadratic polynomial (8x^2 ˗ 4) and verify the relation between the zeroes and the coefficients

Find the zeroes of the quadratic polynomial (5y^2 + 10y) and verify the relation between the zeroes and the coefficients.

Find the zeroes of the quadratic polynomial (3x^2 ˗ x ˗ 4) and verify the relation between the zeroes and the coefficients.

Find the quadratic polynomial whose zeroes are 2/3 and -1/4. Verify the relation between the coefficients and the zeroes of the polynomial.

Find the quadratic polynomial whose zeroes are 2/3 and -1/4 Verify the relation between the coefficients and the zeroes of the polynomial.

Find the quadratic polynomial, sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.

Find the quadratic polynomial, sum of whose zeroes is 0 and their product is -1. Hence, find the zeroes of the polynomial.

Find the quadratic polynomial, sum of whose zeroes is ( 5/2 ) and their product is 1. Hence, find the zeroes of the polynomial.

Find the quadratic polynomial, sum of whose zeroes is sqrt2 and their product is (1/3).

If x =2/3 and x = -3 are the roots of the quadratic equation ax^2+2ax+5x  then find the value of a and b.

If (x+a) is a factor of the polynomial 2x^2 + 2ax + 5x + 10, find the value of a.

One zero of the polynomial 3x^3+16x^2 +15x-18 is 2/3 . Find the other zeros of the  polynomial.

#### Chapter 2: Polynomials solutions [Page 0]

Verify that 3, -2, 1 are the zeros of the cubic polynomial p(x) = (x^3 – 2x2 – 5x + 6) and verify the relation between it zeros and coefficients.

Verify that 5, -2 and 13 are the zeroes of the cubic polynomial p(x) = (3x^3 – 10x^2 – 27x + 10) and verify the relation between its zeroes and coefficients.

Find a cubic polynomial whose zeroes are 2, -3and 4.

Find a cubic polynomial whose zeroes are 1/2, 1 and -3.

Find a cubic polynomial with the sum of its zeroes, sum of the products of its zeroes taken two at a time and the product of its zeroes as 5, -2 and -24 respectively.

If f(x) =x^3-3x+5x-3 is divided by g(x)=x^2-2

If f(x) = x^4 – 3x^2 + 4x + 5 is divided by g(x)= x^2 – x + 1

If f(x) = x^4– 5x + 6" is divided by g(x) "= 2 – x2

By actual division, show that x2 – 3 is a factor of 2x^4 + 3x^3 – 2x^2 – 9x – 12.

On dividing 3x^3 + x^2 + 2x + 5 is divided by a polynomial g(x), the quotient and remainder are (3x – 5) and (9x + 10) respectively. Find g(x).

Verify division algorithm for the polynomial f(x)= (8 + 20x + x^2 – 6x^3) by g(x) =( 2 + 5x –3x^2).

It is given that –1 is one of the zeroes of the polynomial x^3 + 2x^2 – 11x – 12. Find all the zeroes of the given polynomial.

If 1 and –2 are two zeroes of the polynomial (x^3 – 4x^2 – 7x + 10), find its third zero.

If 3 and –3 are two zeroes of the polynomial (x^4 + x^3 – 11x^2 – 9x + 18), find all the zeroes of the given polynomial.

If 2 and -2 are two zeroes of the polynomial (x^4 + x^3 – 34x^2 – 4x + 120), find all the zeroes of the given polynomial.

Find all the zeroes of (x^4 + x^3 – 23x^2 – 3x + 60), if it is given that two of its zeroes are sqrt3 and –sqrt3.

Find all the zeroes of (2x^4 – 3x^3 – 5x2 + 9x – 3), it is being given that two of its zeroes are sqrt3 and –sqrt3.

Obtain all other zeroes of (x^4 + 4x^3 – 2x^2 – 20x – 15) if two of its zeroes are sqrt5 and –sqrt5.

Find all the zeroes of polynomial (2x^4 – 11x^3 + 7x^2 + 13x – 7), it being given that two of its zeroes are (3 + sqrt2) and (3 – sqrt2).

#### Chapter 2: Polynomials solutions [Page 0]

If one zero of the polynomial x^2-4x+1 is (2+sqrt3) , write the other zero.

Find the zeroes of the polynomial x^2 + x – p(p + 1)

Find the zeroes of the polynomial x^2 – 3x – m(m + 3)

Find ∝ , β are the zeros of polynomial ∝ +β= 6 and ∝β 4 then write the polynomial.

If one zero of the quadratic polynomial kx^2 + 3x + k is 2, then find the value of k.

If 3 is a zero of the polynomial 2x^2 + x + k, find the value of k.

If -4 is a zero of the polynomial x^2 – x – (2k + 2) is –4, then find the value of k.

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

If -2 is a zero of the polynomial 3x^2 + 4x + 2k then find the value of k.

Write the zeros of the polynomial f(x) = x^2 – x – 6.

If the sum of the zeros of the quadratic polynomial kx^2-3x + 5 is 1 write the value of k..

If the sum of the zeros of the quadratic polynomial kx^2-3x + 5 is 1 write the value of k..

If (x + a) is a factor of (2x^2 + 2ax + 5x + 10), then find the value of a.

If (a-b) , a and (a + b) are zeros of the polynomial 2x^3-6x^2+5x-7 write the value of a.

If x^3+ x^2-ax + b is divisible by (x^2-x),write the value of a and b.

If 𝛼 and 𝛽 be the zeroes of the polynomial 2x^2 - 7x + k write the value of (𝛼 + 𝛽+ 𝛼 𝛽.

State Division Algorithm for Polynomials.

Find the sum of the zeros and the product of zeros of a quadratic polynomial, are −1/2 and \ -3 respectively. Write the polynomial.

Find the zeroes of the quadratic polynomial f(x) = 6x^2 – 3.

Find the zeroes of the quadratic polynomial f(x) = 4sqrt3x^2 + 5x – 2sqrt3.

If 𝛼, 𝛽 are the zeroes of the polynomial f(x) = x^2 – 5x + k such that 𝛼 - 𝛽 = 1, find the value  of k = ?

If ∝ and β are the zeros of the polynomial f(x) = 6x^2 + x - 2 find the value of (∝/β+∝/β)

If 𝛼, 𝛽 are the zeroes of the polynomial f(x) = 5x^2 -7x + 1 then 1/∝+1/β=?

If 𝛼, 𝛽 are the zeroes of the polynomial f(x) = x2 + x – 2, then (∝/β-∝/β)

If the zeroes of the polynomial f(x) = x^3 – 3x^2 + x + 1 are (a – b), a and (a + b), find the values of a and b.

## R.S. Aggarwal solutions for Class 10 Mathematics chapter 2 - Polynomials

R.S. Aggarwal solutions for Class 10 Maths chapter 2 (Polynomials) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Secondary School Mathematics for Class 10 (for 2019 Examination) solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 10 Mathematics chapter 2 Polynomials are Introduction to Polynomials, Geometrical Meaning of the Zeroes of a Polynomial, Relationship Between Zeroes and Coefficients of a Polynomial, Division Algorithm for Polynomials, Polynomials Examples and Solutions.

Using R.S. Aggarwal Class 10 solutions Polynomials exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in R.S. Aggarwal Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 10 prefer R.S. Aggarwal Textbook Solutions to score more in exam.

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