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​

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Nick 2 months 2021-08-28T07:49:51+00:00 1 Answers 0 views 0

Answers ( )

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    2021-08-28T07:51:48+00:00

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    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 comment

    When (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.

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