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3 years ago

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

Mathematics

2 answers:

Licemer1 [7]3 years ago

5 0

Answer:

x = -7

Step-by-step explanation:

Our function is $f(x) =(x+4)^6(x+7)^5$ . Notice that our possible roots are when x + 4 = 0 and when x + 7 = 0. So, our roots are -4 and -7.

However, the power above x + 4 is even, meaning the graph will simply <em>touch</em> the x-axis at x = -4, but not pass through. The power above x + 7, though, is odd, which means the graph will <em>cross</em> the x-axis.

Thus, the answer is x = -7.

devlian [24]3 years ago

3 0

Answer:

x = -7

Step-by-step explanation:

f(x) = (x+4)⁶(x + 7)⁵

The roots are when f(x) = 0

(x+4)⁶ = 0

x = -4 (multiplicity 6)

(x+7)⁵ = 0

x = -7 (multiplicity 5)

The graph is tangential to the x-axis on roots with even multiplicity, crosses tge x-axis at roots with odd multiplicity

This graph cuts/crosses the x-axis at x = -7

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Step-by-step explanation:

First use Pythagorean theorem to find the length of the hypotenuse. Use $a^2 + b^2 = c^2$ . Since we know a and b we can plug in to find c. When we plug in we get: $(7)^2 + (24)^2 = c^2$ . When we solve this out we get 25 = c.

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