Question

Suppose you need to graph the function f(x) = x(4x + 7)(x - 1)^7. Are there going to be any repeated zeros?

Answer 1

yes

Explanation:

hello,

as we have

`(x-1)^7`

the zero 1 is repeated 7 times

hope this helps

Answer 2

yes

Explanation:

The exponent on each factor tells you the number of times it is repeated. The zero represented by the factor (x -1)⁷ is repeated 7 times.

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When a zero is repeated, the graph is flattened there. The more times it is repeated, the "flatter" the function is at that point. If the repeat-count is even, the graph touches the axis, but does not cross. Here, the repeat-count is odd, so the graph flattens out at the x-intercept, and crosses the x-axis.