NCERT Solutions for class 10 Maths Chapter 2 Exercise 2.1 Polynomials / Bahupad in Hindi Medium and English Medium free. These solutions are updated according to new CBSE Syllabus 2018-19 for CBSE / Uttarakhand & UP Board NCERT Books studying students. Download (Exercise 2.1) in PDF form or use it online given below.
NCERT Solutions for class 10 Maths Chapter 2 Exercise 2.1
Class 10 Maths Solutions Chapter 2 Exercise 2.1 in English Medium
NCERT Solutions for class 10 Maths Chapter 2 Exercise 2.1 Polynomials in English medium to study online. All the solutions are updated for both UP Board and CBSE board. Click here to get Class 10 Maths Chapter 2 Solutions. CLICK HERE for Hindi Medium Solutions.
Class 10 Maths Solutions Chapter 2 Exercise 2.1 in Hindi Medium
NCERT Solutions for class 10 Maths Chapter 2 Exercise 2.1 Polynomials in Hindi to use it online. If you find any difficulty or error in these solutions, please inform us. Click here to get Class 10 Maths Chapter 2 Solutions. Go back to English Medium Solutions.
Important Terms related to Polynomials
- 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.
- Polynomials of degree 1, 2 and 3 are called linear, quadratic and cubic polynomials respectively.
- A quadratic polynomial is an algebraic expression of the form ax² + bx + c, where a, b, c are real numbers with a ≠ 0.
- 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.
- 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)]
- 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
- 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.
- 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
- 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]
- Find the quadratic polynomial whose zeroes are 5 + 2√3 and 5 – 2√3. [Answer: x² – 10x + 13]
- For what value of p, is – 4 a zero of the polynomial x² – 2x – (7p + 3)? [Answer: 3]
- If one zero of p(x) = 4x² – (8k2 – 40k) x – 9 is negative of the other, find values of k. [Answer: k = 0, 5]
- What number should be added to the polynomial x² – 5x + 4, so that 3 is a zero of polynomial so obtained? [Answer: 2]