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At which root does the graph of f(x) = (x + 4)^6(x + 7)^5 cross the x axis?

User Anaa
by
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2 Answers

4 votes

Answer:

The Graph crosses at x -7

Explanation:


User Johnmastroberti
by
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0 votes
ANSWER

The graph of

f(x) = {(x + 4)}^(6) {(x + 7)}^(5)
crosses the x-axis at

x = - 7


EXPLANATION



The nature of the multiplicity of a given polynomial function determines whether the graph crosses the x-axis at that intercept or not?





f(x) = {(x + 4)}^(6) {(x + 7)}^(5)

If the multiplicity of the factor is even as in

{(x + 4)}^(6)
the graph touches but does not cross the x-axis at the intercept where

x = - 4
This means that the x-axis is a tangent to the function at this point.



However, if the multiplicity is odd, as in

({x + 7})^(5)
the graph crosses the x-axis at the intercept where

x = - 7
User Starmaster
by
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