Question

the graph of the polynomial p(x) cut the x-axis 5 times and touches it 3 times . The number of zeroes of p(x) is :​

Answer 1

Answer:

5 because it is decided by how much times it cuts the x-axis

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Answer 2

Given:

The graph of the polynomial p(x) cuts the x-ais 5 times and touches the x-axis 3 times.

To Find:

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

Solution:

The given problem can be solved using the concepts of polynomials.

1. It is given that the polynomial p(x) cuts the x-axis 5 times and also touches the x-axis 3 times.

2. A polynomial is said to have zeroes when it touches the x-axis. The number of zeroes for the polynomial is equal to the number of times it touches/cuts the x-axis.

3. If the graph either touches/ intersects with the x-axis it is considered as a zero of the polynomial.

For example, the line y=x intersects the x-axis 1 time, hence it has 1 root. The line x^2 touches the x-axis only once so it has only one root.

4. It is given that the graph cuts the x-axis 5 times and touches the x-axis 3 times. Hence, the total number of zeroes is the sum of the above intersections/touches with the x-axis.

=> Total number of zeroes = 5 intersections + 3 touches with the x-axis,

=> Total number of zeroes = 8.

Therefore, the total number of zeroes of p(x) is 8.