answer A . -7
Odd exponents cross the x-axis , even exponents touch the x-axis
When x=-4 x=-7
x = -7
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
x = -7
Our function is . 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 touch the x-axis at x = -4, but not pass through. The power above x + 7, though, is odd, which means the graph will cross the x-axis.
Thus, the answer is x = -7.
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