Share

## Zeroes of a polynomial can be determined graphically. Number of zeroes of a polynomial is equal to number of points where the graph of polyn

Question

Zeroes of a polynomial can be determined graphically. Number of zeroes of a polynomial is equal to number of points where the graph of polynomial.

2 points

a. intersects y-axis

b. intersects x-axis

c. intersects y-axis or intersects x-axis

d. none of these

in progress
0

Mathematics
2 months
2021-08-28T07:49:51+00:00
2021-08-28T07:49:51+00:00 1 Answers
0 views
0
## Answers ( )

9514 1404 393

Answer:b. intersects x-axis

Step-by-step explanation:A zero of the polynomial is where y = 0. The equation y = 0 is the equation of the x-axis, so intersections of the graph of the function with the x-axis are places where the function value is zero.

The number of (distinct real) zeros is equal to the number of points where the graph intersects the x-axis._____

Additional commentWhen (x -p)^n is a factor of the polynomial, the graph will intersect the x-axis at x=p. The zero is said to have “multiplicity n”. For odd values of n, the graph will cross the x-axis (change sign) at x=p. For even values of n, the graph will touch the axis at x=p, but will not cross there.

So, the number of intersections with the x-axis tells the number of

distinct real zeros, but does not say anything about their multiplicity. Complex zeros will not cause the graph to touch the x-axis.