Question

The above shows part of the graph of the function $y=0.1x^5-x^3$
You can see $3$ roots ... what are their multiplicities (from left to right)?

• A. $1,1$ and $1$
• B. $2,1$ and $2$
• C. $1,3$ and $1$
• D. $-3,0$ and $3$

Answer 1

The correct option is C $1,3$ and $1$

Given $y=0.1x^5-x^3$

$\Rightarrow y=x^3(0.1x^2-1)$

$\Rightarrow y=0.1x^3(x-\sqrt{10})(x+\sqrt{10})$

Therefore the roots are $0,\sqrt{10},-\sqrt{10}$ and their respective multiplicities are $3,1,1$

So option $C$ is correct