# NCERT Solutions for class 10 Maths Chapter 2 Exercise 2.1

NCERT Solutions for class 10 Maths Chapter 2 Exercise 2.1 Polynomials / बहुपद Hindi Medium and English Medium download in PDF form or View in Video Format free for new academic session 2020-2021.

Offline Solutions Apps 2020-21 are updated according to new CBSE Syllabus 2020-21 for Gujrat Board, CBSE / Uttarakhand & UP Board students studying NCERT Books 2020-21. Download (Exercise 2.1) in PDF form or use it online without download.## NCERT Solutions for class 10 Maths Chapter 2 Exercise 2.1

Class: | 10 |

Subject: | Maths – गणित |

Chapter 2: | Exercise 2.1 |

### 10 Maths Chapter 2 Exercise 2.1 Solutions

NCERT Solutions for class 10 Maths Chapter 2 Exercise 2.1 Polynomials in Hindi and English medium to use it online or download in PDF. If you find any difficulty or error in these solutions, please inform us. We are here to help you in education without any charges.

### Class 10 Maths Exercise 2.1 Solutions

#### Important Terms related to Polynomials

1. Polynomial: If x is a variable, n is a natural number and a0, a1, a2, a3, ………. an are real numbers, then p(x) = an x^n + a^n-1. X^x-1 + ……… + a1 x + a0, (an ≠ 0) is called a polynomial in x.

2. Polynomials of degree 1, 2 and 3 are called linear, quadratic and cubic polynomials respectively.

3. A quadratic polynomial is an algebraic expression of the form ax² + bx + c, where a, b, c are real numbers with a ≠ 0.

4. Zeroes of a polynomial p(x) are precisely the x – coordinates of the points where the graph of y = p(x) intersects the x–axis, i.e., x = a is a zero of polynomial p(x) if p(a) = 0.

5. Division Algorithm states that given any polynomials p(x) and g(x), there exist polynomial q(x) and r(x) such that: p(x) = g(x). q(x) + r(x) ; g(x) ≠ 0, [where either r(x) = 0 or degree r(x) < degree g(x)]
6. A polynomial can have at most the same number of zeroes as the degree of the polynomial.
7. Relationship between zeroes and coefficients of a polynomial. If m and n are zeroes of p(x) ax² + bx + c (a ≠ 0), them Sum of zeroes = m + n = – b/a, Product of zeroes = mn = c/a
8. If m, n are zeroes of a quadratic polynomial p(x), then p(x) = k[x² – (sum of zeroes) x + product of zeroes] or p(x) = k [x² – (m + n)x +mn]; where k is any non-zero real number.
9. Graph of linear polynomial p(x) = ax + b is a straight line.
(i) If one zero of a quadratic polynomial p(x) is negative of the other, then coefficient of x = 0. (ii) If zeroes of a quadratic polynomial p(x) are reciprocal of each other, then co-efficient of x² = constant term.

##### IMPORTANT QUESTIONS BASED ON POLYNOMIALS

1. What will be the number of zeroes of a linear polynomial p(x) if its graph (i) passes through the origin. (ii) doesn’t intersect or touch x-axis at any point? [Answer: (i) 1, (ii) 0]

2. Find the quadratic polynomial whose zeroes are 5 + 2√3 and 5 – 2√3. [Answer: x² – 10x + 13]

3. For what value of p, is – 4 a zero of the polynomial x² – 2x – (7p + 3)? [Answer: 3]

4. If one zero of p(x) = 4x² – (8k2 – 40k) x – 9 is negative of the other, find values of k. [Answer: k = 0, 5]

5. What number should be added to the polynomial x² – 5x + 4, so that 3 is a zero of polynomial so obtained? [Answer: 2]

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