Which statement describes the graph of f(x) = 4x⁷ + 40x⁶ + 100x⁵?
The graph crosses the x axis at x = 0 and touches the x axis at x = 5.
The graph touches the x axis at x = 0 and crosses the x axis at x = 5.
The graph crosses the x axis at x = 0 and touches the x axis at x = -5.
The graph touches the x axis at x = 0 and crosses the x axis at x = -5.

Solution:

Given f(x) = 4x⁷ + 40x⁶ + 100x⁵

It can be written as

f(x) = 4x⁵ (x² + 10x + 25)

Here

4x⁵ = 0 or x² + 10x + 25 = 0

By further simplification

x = 0 or (x + 5)² = 0

So we get

x = 0 or x = -5

Therefore, the graph crosses the x axis at x = 0 and touches the x axis at x = -5.

Which statement describes the graph of f(x) = 4x⁷ + 40x⁶ + 100x⁵?

Summary:

The statement “the graph crosses the x axis at x = 0 and touches the x axis at x = -5” describes the graph of f(x) = 4x⁷ + 40x⁶ + 100x⁵.