#### Chapters

Chapter 2 - Polynomials

Chapter 3 - Pair of Linear Equations in Two Variables

Chapter 4 - Triangles

Chapter 5 - Trigonometric Ratios

Chapter 6 - Trigonometric Identities

Chapter 7 - Statistics

Chapter 8 - Quadratic Equations

Chapter 9 - Arithmetic Progression

Chapter 10 - Circles

Chapter 11 - Constructions

Chapter 12 - Trigonometry

Chapter 13 - Probability

Chapter 14 - Co-Ordinate Geometry

Chapter 15 - Areas Related to Circles

Chapter 16 - Surface Areas and Volumes

## Chapter 2 - Polynomials

#### Page 0

find the zeroes of the quadratic polynomial x^{2} – 2x – 8 and verify a relationship between zeroes and its coefficients

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

4s^{2} – 4s + 1

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

t^{2} – 15

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

`p(x) = x^2 + 2sqrt2x + 6`

`q(x)=sqrt3x^2+10x+7sqrt3`

`f(x)=x^2-(sqrt3+1)x+sqrt3`

`g(x)=a(x^2+1)-x(a^2+1)`

`6x^2-3-7x`

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α - β

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha-1/beta`

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha+1/beta-2alphabeta`

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α^{2}β + αβ^{2}

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α^{4} + β^{4}

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/(aalpha+b)+1/(abeta+b)`

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `beta/(aalpha+b)+alpha/(abeta+b)`

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate

`a[alpha^2/beta+beta^2/alpha]+b[alpha/beta+beta/alpha]`

If α and β are the zeros of the quadratic polynomial f(x) = 6x^{2} + x − 2, find the value of `alpha/beta+beta/alpha`

If a and are the zeros of the quadratic polynomial f(x) = 𝑥^{2} − 𝑥 − 4, find the value of `1/alpha+1/beta-alphabeta`

If 𝛼 and 𝛽 are the zeros of the quadratic polynomial p(x) = 4x^{2} − 5x −1, find the value of α^{2β} + αβ^{2}.

If a and 3 are the zeros of the quadratic polynomial f(x) = x^{2} + x − 2, find the value of `1/alpha-1/beta`

If 𝛼 and 𝛽 are the zeros of the quadratic polynomial f(x) = x^{2} − 5x + 4, find the value of `1/alpha+1/beta-2alphabeta`

If 𝛼 and 𝛽 are the zeros of the quadratic polynomial f(t) = t^{2} − 4t + 3, find the value of `alpha^4beta^3+alpha^3beta^4`

If α and β are the zeros of the quadratic polynomial p(y) = 5y^{2} − 7y + 1, find the value of `1/alpha+1/beta`

If α and β are the zeros of the quadratic polynomial p(s) = 3s^{2} − 6s + 4, find the value of `alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta`

If α and β are the zeros of the quadratic polynomial f(x) = x^{2} − px + q, prove that `alpha^2/beta^2+beta^2/alpha^2=p^4/q^2-(4p^2)/q+2`

If the squared difference of the zeros of the quadratic polynomial f(x) = x^{2} + px + 45 is equal to 144, find the value of p.

If the sum of the zeros of the quadratic polynomial f(t) = kt^{2} + 2t + 3k is equal to their product, find the value of k.

If one zero of the quadratic polynomial f(x) = 4x^{2} − 8kx − 9 is negative of the other, find the value of k.

If α and β are the zeros of the quadratic polynomial f(x) = x^{2} − 1, find a quadratic polynomial whose zeroes are `(2alpha)/beta" and "(2beta)/alpha`

If α and β are the zeros of the quadratic polynomial f(x) = x^{2} − 3x − 2, find a quadratic polynomial whose zeroes are `1/(2alpha+beta)+1/(2beta+alpha)`

If α and β are the zeros of a quadratic polynomial such that α + β = 24 and α − β = 8, find a quadratic polynomial having α and β as its zeros.

If α and β are the zeros of the quadratic polynomial f(x) = x^{2} − p (x + 1) — c, show that (α + 1)(β +1) = 1− c.

If If α and β are the zeros of the quadratic polynomial f(x) = x^{2} – 2x + 3, find a polynomial whose roots are α + 2, β + 2.

If If α and β are the zeros of the quadratic polynomial f(x) = x^{2} – 2x + 3, find a polynomial whose roots are `(alpha-1)/(alpha+1)` , `(beta-1)/(beta+1)`

If α and β are the zeroes of the polynomial f(x) = x^{2} + px + q, form a polynomial whose zeroes are (α + β)^{2} and (α − β)^{2}.

#### Page 0

Verify that the numbers given along side of the cubic polynomials are their zeroes. Also verify the relationship between the zeroes and the coefficients.

`2x^3 + x^2 – 5x + 2 ; 1/2, 1, – 2`

Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case

x^{3} – 4x^{2} + 5x – 2; 2, 1, 1

Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and product of its zeros as 3, −1 and −3 respectively.

If the zeros of the polynomial f(x) = 2x^{3} − 15x^{2} + 37x − 30 are in A.P., find them.

Find the condition that the zeros of the polynomial f(x) = x^{3} + 3px^{2} + 3qx + r may be in A.P.

If the zeros of the polynomial f(x) = ax^{3} + 3bx^{2} + 3cx + d are in A.P., prove that 2*b*^{3} − 3*abc* + *a*^{2}*d* = 0.

If the zeros of the polynomial f(x) = x^{3} − 12x^{2} + 39x + k are in A.P., find the value of *k*.

#### Page 0

Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in the following f(x) = x^{3} − 6x^{2} + 11x − 6, g(x) = x^{2} + x + 1

Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in the following f(x) = 10x^{4} + 17x^{3} − 62x^{2} + 30x − 3, g(x) = 2x^{2} + 7x + 1

Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in the following f(x) = 4x^{3}^{ }+ 8x^{2} + 8x + 7, g(x) = 2x^{2} − x + 1

Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in the following f(x) = 15x^{3} − 20x^{2} + 13x − 12; g(x) = x^{2} − 2x + 2

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial

t^{2} – 3, 2t^{4} + 3t^{3} – 2t^{2} – 9t – 12

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial

x^{3} – 3x + 1, x^{5} – 4x^{3} + x^{2} + 3x + 1

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm g(x) = 2x^{2} − x + 3, f(x) = 6x^{5} − x^{4} + 4x^{3} − 5x^{2} − x − 15

Obtain all zeros of the polynomial *f*(*x*) = 2*x*^{4} + *x*^{3} − 14*x*^{2} − 19*x* − 6, if two of its zeros are −2 and −1.

Obtain all zeros of the polynomial *f*(*x*) = 2*x*^{4} + *x*^{3} − 14*x*^{2} − 19*x* − 6, if two of its zeros are −2 and −1.

Obtain all zeros of the polynomial *f*(*x*) = 2*x*^{4} + *x*^{3} − 14*x*^{2} − 19*x* − 6, if two of its zeros are −2 and −1.

Obtain all zeros of f(x) = x^{3} + 13x^{2} + 32x + 20, if one of its zeros is −2.

Obtain all zeros of the polynomial f(x) = x^{4} − 3x^{3} − x^{2} + 9x − 6, if two of its zeros are `-sqrt3` and `sqrt3`

Find all zeros of the polynomial *f*(*x*) = 2*x*^{4} − 2*x*^{3} − 7*x*^{2} + 3*x* + 6, if its two zeros are `-sqrt(3/2)` and `sqrt(3/2)`

What must be added to the polynomial f(x) = x^{4} + 2x^{3} − 2x^{2} + x − 1 so that the resulting polynomial is exactly divisible by x^{2} + 2x − 3 ?

What must be subtracted from the polynomial f(x) = x^{4} + 2x^{3} − 13x^{2} − 12x + 21 so that the resulting polynomial is exactly divisible by x^{2} − 4x + 3 ?

Find all the zeros of the polynomial x^{4} + x^{3} − 34x^{2} − 4x + 120, if two of its zeros are 2 and −2.

Find all zeros of the polynomial 2x^{4} + 7x^{3} − 19x^{2} − 14x + 30, if two of its zeros are `sqrt2` and `-sqrt2`.

Find all the zeros of the polynomial 2x^{3} + x^{2} − 6x − 3, if two of its zeros are `-sqrt3` and `sqrt3`

Find all the zeros of the polynomial x^{3} + 3x^{2} − 2x − 6, if two of its zeros are `-sqrt2` and `sqrt2`

#### Textbook solutions for Class 10

## R.D. Sharma solutions for Class 10 Mathematics chapter 2 - Polynomials

R.D. Sharma solutions for Class 10 Mathematics chapter 2 (Polynomials) include all questions with solution and detail explanation from 10 Mathematics. 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 created the CBSE 10 Mathematics 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 Geometrical Meaning of the Zeroes of a Polynomial, Division Algorithm for Polynomials, Polynomials Examples and Solutions, Introduction to Polynomials, Relationship Between Zeroes and Coefficients of a Polynomial.

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