In mathematics, a polynomial is an expression consisting of variables (or indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. An example of a polynomial of a single indeterminate (or variable), x, is x^{2} - 4x + 7, which is a quadratic polynomial.

Polynomials appear in a wide variety of areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated problems in the sciences; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, central concepts in algebra and algebraic geometry.

Polynomials appear in a wide variety of areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated problems in the sciences; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, central concepts in algebra and algebraic geometry.

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**Exercise 2.1 : ** Solutions of Questions on Page Number : **28**

Q1 :
**
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**Exercise 2.2 : ** Solutions of Questions on Page Number : **33**

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**Exercise 2.3 2.4 : ** Solutions of Questions on Page Number : **36**

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**Exercise 2.4 : ** Solutions of Questions on Page Number : **37**

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**Popular Articles**

The graphs of *y* = *p*(*x*) are given in
following figure, for some polynomials *p*(*x*). Find
the number of zeroes of *p*(*x*), in each case.

(i)

(ii)

(iii)

(iv)

(v)

(v)

**Answer :**

(i) The number of zeroes is 0 as the graph does not cut the
*x*-axis at any point.

(ii) The number of zeroes is 1 as the graph intersects the
*x*-axis at only 1 point.

(iii) The number of zeroes is 3 as the graph intersects the
*x*-axis at 3 points.

(iv) The number of zeroes is 2 as the graph intersects the
*x*-axis at 2 points.

(v) The number of zeroes is 4 as the graph intersects the
*x*-axis at 4 points.

(vi) The number of zeroes is 3 as the graph intersects the
*x*-axis at 3 points.

Answer needs Correction? Click Here

Q1 :
**
**

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

**Answer :**

The value of is zero when *x*
- 4 = 0 or *x* +
2 = 0, i.e., when *x* = 4 or *x* =
- 2

Therefore, the zeroes of are 4 and - 2.

Sum of zeroes =

Product of zeroes

The value of 4*s*^{2}
- 4*s* + 1 is
zero when 2*s* -
1 = 0, i.e.,

Therefore, the zeroes of 4*s*^{2}
- 4*s* + 1
areand.

Sum of zeroes =

Product of zeroes

The value of 6*x*^{2}
- 3
- 7*x* is zero
when 3*x* + 1 = 0 or 2*x*
- 3 = 0, i.e.,
or

Therefore, the zeroes of 6*x*^{2}
- 3
- 7*x*
are.

Sum of zeroes =

Product of zeroes =

The value of 4*u*^{2} + 8*u* is zero when
4*u* = 0 or *u* + 2 = 0, i.e., *u* = 0 or *u*
= - 2

Therefore, the zeroes of 4*u*^{2} + 8*u* are 0
and - 2.

Sum of zeroes =

Product of zeroes =

The value of *t*^{2}
- 15 is zero when
or , i.e., when

Answer needs Correction? Click Here

Q2 :
**
**

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

**Answer :**

Q1 :
**
**

Divide the polynomial *p*(*x*) by the polynomial
*g*(*x*) and find the quotient and remainder in each of
the following:

(i)

(ii)

(iii)

**Answer :**

Q2 :
**
**

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:

**Answer :**

Q3 :
**
**

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

**Answer :**

Q4 :
**
**

Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, - 7, - 14 respectively.

**Answer :**

Q5 :
**
**

Obtain all other zeroes of , if two of its zeroes are .

**Answer :**

Q6 :
**
**

On dividing by a polynomial
*g*(*x*), the quotient and remainder were *x*
- 2 and
- 2*x* + 4,
respectively. Find *g*(*x*).

**Answer :**

Q7 :
**
**

Give examples of polynomial *p*(*x*),
*g*(*x*), *q*(*x*) and *r*(*x*),
which satisfy the division algorithm and

(i) deg
*p*(*x*) =
deg
*q*(*x*)

(ii) deg
*q*(*x*) =
deg
*r*(*x*)

(iii) deg
*r(x*) = 0

**Answer :**

Q1 :
**
**

If the zeroes of polynomial are, find *a* and
*b*.

**Answer :**

Q2 :
**
**

**]**It two zeroes of the polynomial are, find other zeroes.

**Answer :**

Q3 :
**
**

If the polynomial is
divided by another polynomial, the
remainder comes out to be *x* + *a*, find *k* and
*a*.

**Answer :**

Maths : CBSE ** NCERT ** Exercise Solutions for Class 10th for ** Polynomials ** ( Exercise 2.1, 2.2, 2.3 2.4, 2.4 ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

- 10th Maths Paper Solutions Set 2 : CBSE Delhi Previous Year 2015
- 10th Maths Paper Solutions Set 3 : CBSE Delhi Previous Year 2015
- 10th Maths Paper Solutions Set 1 : CBSE Delhi Previous Year 2015
- 10th Maths Paper Solutions Set 1 : CBSE Abroad Previous Year 2015
- 10th Maths Paper Solutions Set 1 : CBSE All India Previous Year 2015

- Chapter 3 - Pair of Linear Equations in Two Variables Class 10
- Chapter 1 - Real Numbers Class 10
- Chapter 6 - Triangles Class 10
- Chapter 8 - Introduction to Trigonometry Class 10
- Chapter 13 - Surface Areas and Volumes Class 10
- Chapter 4 - Quadratic Equations Class 10
- Chapter 14 - Statistics Class 10
- Chapter 9 - Some Applications of Trigonometry Class 10
- Chapter 5 - Arithmetic Progressions Class 10

Exercise 2.1 |

Question 1 |

Exercise 2.2 |

Question 1 |

Question 2 |

Exercise 2.3 2.4 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Exercise 2.4 |

Question 1 |

Question 2 |

Question 3 |