#### 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

#### RD Sharma 10 Mathematics

## 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`

#### RD Sharma 10 Mathematics

#### Textbook solutions for Class 10th Board Exam

## RD Sharma solutions for Class 10th Board Exam Mathematics chapter 2 - Polynomials

RD Sharma solutions for Class 10th Board Exam 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 10 Mathematics solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 10th Board Exam 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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