# RS Aggarwal solutions for Secondary School Class 10 Maths chapter 2 - Polynomials [Latest edition]

## Chapter 2: Polynomials

Exercises 1Exercises 2Exercises 3
Exercises 1

### RS Aggarwal solutions for Secondary School Class 10 Maths Chapter 2 Polynomials Exercises 1

Exercises 1 | Q 1

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

Exercises 1 | Q 2

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

Exercises 1 | Q 3

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

Exercises 1 | Q 4

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

Exercises 1 | Q 5

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.

Exercises 1 | Q 6

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

Exercises 1 | Q 7

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

Exercises 1 | Q 8

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

Exercises 1 | Q 9

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

Exercises 1 | Q 10

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

Exercises 1 | Q 11

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

Exercises 1 | Q 12

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

Exercises 1 | Q 13

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

Exercises 1 | Q 14

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

Exercises 1 | Q 15

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

Exercises 1 | Q 16

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

Exercises 1 | Q 17

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

Exercises 1 | Q 18

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

Exercises 1 | Q 19

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.

Exercises 1 | Q 20

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

Exercises 1 | Q 21

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

Exercises 2

### RS Aggarwal solutions for Secondary School Class 10 Maths Chapter 2 Polynomials Exercises 2

Exercises 2 | Q 1

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.

Exercises 2 | Q 2

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.

Exercises 2 | Q 3

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

Exercises 2 | Q 4

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

Exercises 2 | Q 5

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.

Exercises 2 | Q 6

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

Exercises 2 | Q 7

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

Exercises 2 | Q 8

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

Exercises 2 | Q 9

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

Exercises 2 | Q 10

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).

Exercises 2 | Q 11

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

Exercises 2 | Q 12

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.

Exercises 2 | Q 13

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

Exercises 2 | Q 14

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.

Exercises 2 | Q 15

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.

Exercises 2 | Q 16

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.

Exercises 2 | Q 17

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.

Exercises 2 | Q 18

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

Exercises 2 | Q 19

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).

Exercises 3

### RS Aggarwal solutions for Secondary School Class 10 Maths Chapter 2 Polynomials Exercises 3

Exercises 3 | Q 1

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

Exercises 3 | Q 2

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

Exercises 3 | Q 3

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

Exercises 3 | Q 4

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

Exercises 3 | Q 5

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

Exercises 3 | Q 6

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

Exercises 3 | Q 7

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

Exercises 3 | Q 8

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

Exercises 3 | Q 9

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

Exercises 3 | Q 10

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

Exercises 3 | Q 11

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

Exercises 3 | Q 12

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

Exercises 3 | Q 13

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

Exercises 3 | Q 14

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

Exercises 3 | Q 15

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

Exercises 3 | Q 16

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

Exercises 3 | Q 17

State Division Algorithm for Polynomials.

Exercises 3 | Q 18

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

Exercises 3 | Q 19

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

Exercises 3 | Q 20

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

Exercises 3 | Q 21

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 = ?

Exercises 3 | Q 22

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

Exercises 3 | Q 23

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

Exercises 3 | Q 24

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

Exercises 3 | Q 25

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.

## Chapter 2: Polynomials

Exercises 1Exercises 2Exercises 3

## RS Aggarwal solutions for Secondary School Class 10 Maths chapter 2 - Polynomials

RS Aggarwal solutions for Secondary School 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 Class 10 Maths solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Secondary School Class 10 Maths chapter 2 Polynomials are Geometrical Meaning of the Zeroes of a Polynomial, Relationship Between Zeroes and Coefficients of a Polynomial, Division Algorithm for Polynomials, Polynomials, Polynomials, Geometrical Meaning of the Zeroes of a Polynomial, Relationship Between Zeroes and Coefficients of a Polynomial, Division Algorithm for Polynomials, Polynomials, Polynomials.

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