The above shows part of the graph of the function $y = - 0.2 (x + 2)^{6} + (x + 2)^{4}$ .
What is the multiplicity of the root at $x = - 2$ ?

2

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4

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6

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Solution

The correct option is B $4$
Given $y = - 0.2 {(x + 2)}^{6} + {(x + 2)}^{4}$
$\Rightarrow y = {(x + 2)}^{4} (1 - 0.2 {(x + 2)}^{2})$
$\Rightarrow y = {(x + 2)}^{4} (- x^{2} - 4 x + 1) \times \frac{1}{5}$
Therefore multiplicity of root at $x = - 2$ is $4$
Therefore correct option is $B$

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The above shows part of the graph of the function y=−0.2(x+2)6+(x+2)4.What is the multiplicity of the root at x=−2?

The correct option is B 4Given y=−0.2(x+2)6+(x+2)4⇒y=(x+2)4(1−0.2(x+2)2)⇒y=(x+2)4(−x2−4x+1)×15Therefore multiplicity of root at x=−2 is 4Therefore correct option is B

The above shows part of the graph of the function $y = - 0.2 (x + 2)^{6} + (x + 2)^{4}$ .
What is the multiplicity of the root at $x = - 2$ ?

The correct option is B $4$
Given $y = - 0.2 {(x + 2)}^{6} + {(x + 2)}^{4}$
$\Rightarrow y = {(x + 2)}^{4} (1 - 0.2 {(x + 2)}^{2})$
$\Rightarrow y = {(x + 2)}^{4} (- x^{2} - 4 x + 1) \times \frac{1}{5}$
Therefore multiplicity of root at $x = - 2$ is $4$
Therefore correct option is $B$