#### Chapters

Chapter 2: Polynomials

Chapter 3: Linear Equations in two variables

Chapter 4: Triangles

Chapter 5: Trigonometric Ratios

Chapter 6: T-Ratios of some particular angles

Chapter 7: Trigonometric Ratios of Complementary Angles

Chapter 8: Trigonometric Identities

Chapter 9: Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive

Chapter 10: Quadratic Equations

Chapter 11: Arithmetic Progression

Chapter 12: Circles

Chapter 13: Constructions

Chapter 14: Height and Distance

Chapter 15: Probability

Chapter 16: Coordinate Geomentry

Chapter 17: Perimeter and Areas of Plane Figures

Chapter 18: Area of Circle, Sector and Segment

Chapter 19: Volume and Surface Area of Solids

#### R.S. Aggarwal Secondary School Mathematics Class 10 (for 2019 Examination)

## 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 – 1`is 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.

## Chapter 2: Polynomials

#### R.S. Aggarwal Secondary School Mathematics Class 10 (for 2019 Examination)

#### Textbook solutions for Class 10

## 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.

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