Question

-13x^2(5x+10)(x-3)

how is 0, 0 a zero?

Answer 1

A "zero" of a function is an x-value where the function equals 0. For f(x) = -13x^2(5x+10)(x-3):

- Plug in x = 0: f(0) = -13·0^2·(5·0+10)·(0-3) = 0.
So x = 0 is a root, and the corresponding point on the graph is (0, 0).

Other roots:
- 5x + 10 = 0 → x = -2, so (-2, 0).
- x - 3 = 0 → x = 3, so (3, 0).

Note on multiplicity:
- x = 0 comes from the factor x^2, so it has multiplicity 2 (even). The graph touches the x-axis at (0,0) and bounces off rather than crossing.
- x = -2 and x = 3 have multiplicity 1, so the graph crosses the x-axis at those points.