A polynomial $y = f (x)$ when represented on graph cuts $x - axis$ at 2 points and $y - axis$ at 3 points. Find the number of zeroes of $f (x)$ .

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Solution

The zeroes of a polynomial are the points which cuts the $x - axis$ on the graph. As $f (x)$ cuts $x - axis$ at 2 points, the number of zeroes are 2.

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List I	List II
(A) $f (x) = cos x$	$1.$ The graph cuts y-axis in infinite number of points
(B) $f (x) = l n x$	$2.$ The graph cut x-axis in two points.
(C) $f (x) = x^{2} - 5 x + 4$	$3.$ The graph cuts y-axis in only one point
(D) $f (x) = e^{x}$	$4.$ The graph cuts x-axis in only one point
	$5.$ The graph cuts x-axis in infinite number of points

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