Question

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

Answer 1

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
$x = - 7$

Answer 2

Answer:

The Graph crosses at x -7

Step-by-step explanation: