Question

The graphs of y = p(x) are given in the figure below, for some polynomials p(x). In each case, find the number of zeros of p(x).

Answer 1

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Condition :

A polynomial p(x) of degree 'n' , the

graph of y = p(x) intersects the X - axis

at almost 'n' points .

So, p(x) of degree 'n' has atmost 'n'

zeroes .

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i ) The line never meet the X +- axis so

the number of zeroes of the polynomial

is zero.

ii ) The curve of the polynomial meet

the Z-axis at only one point .

So, the number of zeroes of the

polynomial is one .

iii ) The curve meet the X-axis at three

point .

So, the number of zeroes of the

polynomial is three.

iv ) The curve meet the X-AXIS at

two points .

So, the number of zeroes of the

polynomial is two.

v ) The curve meet the X-axis at four

points .

So, the number of zeroes of the

polynomial is four .

vi ) The curve meet the X-axis at three

distinct points.

So, the number of zeroes of the

polynomial is three.

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Answer 2

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