Question

The graph of y = p(x), where p(x) is a polynomial in variable x, is as follows:
The number of zeroes of p(x) is​

Answer 1

Question:

The graph of y = p(x) , where p(x) is a polynomial in variable x . Find the number of zeros of the polynomial p(x).

Given:

Graph of the polynomial , y = p(x).

To find:

The number of zeros of the polynomial p(x).

Answer:

The given polynomial p(x) has five zeros.

Note:

• Zeros of a polynomial p(x) are the possible values of "x" for which, the polynomial p(x) becomes zero.

• The degree of polynomial decides the number of zeros.

• The maximum number of zeros of a polynomial is equal to its degree.

• Also, the maximum number of zeros is equal to the number of points at which the graph of polynomial, y = p(x) cuts the x-axis.

Solution:

From the graph of the given polynomial p(x) , it is cutting the x-axis at five points.

Thus,

The number of zeros of the polynomial p(x) is Five.

Moreover,

The degree of the polynomial p(x) is five.

Answer 2

Answer:

$\bold\red{5\:zeroes}$

Step-by-step explanation:

Given,

The graph of y = p(x)

where,

p(x) is a Polynomial in variable x.

Since,

the polynomial p(x) is function of x,

its values depemds on values of x

Now,

For the zeroes of a Polynomial,

we need to find the values of x for which the p(x) becomes zero.

Simply,

we can say that,

The points where y is zero or,

those points where the graph of Polynomial cuts the X - axis are the points for zeroes.

Now,

we can observe that,

the graph has intersected 5 times the X axis.

Hence,

the Number of zeroes for Polynomial p(x) are

5 zeroes