The zeros are 0 and -5/2 with multiplicity 2 and 1 respectively
The root at x = -5/2 has an odd multiplicity of 1, indicating the graph crosses the x-axis at this point.
What is a polynomial?
Given
f(x) -8x³ - 20x²
Factor out
f(x) = -4x²(2x + 5)
set each factor equal to zero:
-4x² = 0 gives a root of x = 0 with multiplicity 2x + 5 = 0 gives a root of x = - 5/2with multiplicity 1.
So, the equation has a zero at x = 0 with multiplicity 2 and a zero at x = -5/2 with multiplicity 1.
To understand the effect on the graph, the multiplicity of a root affects the behavior near that point. A root with an even multiplicity will touch or bounce off the x-axis, while a root with an odd multiplicity will cross the x-axis.
x = 0 has an even multiplicity of 2, suggesting the graph touches the x-axis at that point. The root at x = -5/2 has an odd multiplicity of 1, indicating the graph crosses the x-axis at this point.