Given Class 10 NCERT Solutions for Chapter 2 Polynomials Exercise 2.1 can be used to complete hometask and solve difficult questions. Through the help of CBSE NCERT Solutions for Class 10, you can able to solve the problems efficiently.
Book Name | Class 10 Mathematics NCERT Textbook |
Chapter | Chapter 2 Polynomials |
Exercise | Ex 2.1 |
1. The graphs of y = p(x) are given in the figure given below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.
Solution
(i) The given graph is parallel to x-axis. It does not intersect the x-axis.
∴ It has no zeroes.
(ii) The given graph intersects the x-axis at one point only.
∴ It has one zero.
(iii) The given graph intersects the x-axis at three points.
∴ It has three zeroes.
(iv) The given graph intersects the x-axis at two points.
∴ It has two zeroes.
(v) The given graph intersects the x-axis at four points.
∴ It has four zeroes.
(vi) The given graph meets the x-axis at three points.
∴ It has three zeroes.
Relationship between Zeroes and Coefficients of a Polynomial(i) For a quadratic polynomial: If α and β are the zeroes the quadratic polynomial
p (x) = ax^{2} + bx + c, (a ≠ 0) then
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<!--[endif]-->(ii) For a cubic polynomial: If α, β, γ are the zeroes of a cubic polynomial ax3 + bx2 + cx + d, then
Sum of products of the zeroes taken two at a time = These NCERT Solutions for Class 10 Maths will be very helpful in scoring good marks in the examinations.