Mathematics solution NCERT
Class 10 - Chapter 2: Polynomials
Exercise 2.1
Q1: The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.
(i)
The graph is a horizontal line parallel to the x-axis and does not intersect the x-axis.
Number of zeroes = 0
(ii)
The graph cuts the x-axis at one point.
Number of zeroes = 1
(iii)
The graph cuts the x-axis at three distinct points.
Number of zeroes = 3
(iv)
The graph cuts the x-axis at two distinct points.
Number of zeroes = 2
(v)
The graph cuts the x-axis four times.
Number of zeroes = 4
(vi)
The graph intersects or touches the x-axis at four points.
Number of zeroes = 4
Answer Table
| Graph | Number of Zeroes |
|---|---|
| (i) | 0 |
| (ii) | 1 |
| (iii) | 3 |
| (iv) | 2 |
| (v) | 4 |
| (vi) | 4 |
Jab bhi curve axis ko touch karta hai ya cross karke jata hai uske
utne hi zeros hote hain. Lekin equation dekh lena ki y = f(x) hai ya phir x = f(y).
kyu ki y = f(x) ke case me hume x - axis ko dekhna hota hai ki koi bhi curve
x- axis ko kitni bar kat raha hai. But second case me hume y - axis ko dekhna hota hai.