Q. 54.4( 10 Votes )

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

(i)



(ii)



(iii)


Answer :

Given:


To Find: The number of zeroes of f(x)


Concept Used:


The zero of a polynomial means the point at which y = f(x) = 0, this occurs only at the x–axis.


So, we need to look for the points at which f(x) cuts the x–axis. The number of times f(x) cuts x–axis, that is the number of zeroes of f(x).


Explanation:


(i) We can see that f(x) cuts the x–axis at only one point.


So, number of zeroes of f(x) = 1


(ii) We can see that f(x) cuts the x–axis at 2 points.


So, the number of zeroes of f(x) = 2


(iii) We can see that f(x) cuts the x–axis at 6 points.


So, the number of zeroes of f(x) = 6


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