Answer:
C. He is not correct because the greatest exponent of the system is five so there must be five solutions, three of which must be multiplicities or complex.
Step-by-step explanation:
We are given the equation [tex]x^5=-2x^2[/tex] i.e. [tex]x^5+2x^2=0[/tex].
So, we have a polynomial [tex]x^5+2x^2[/tex] of degree 5.
Fundamental Theorem of Algebra states that 'An n-degree polynomial have 'n' number of roots'.
Thus, the equation [tex]x^5+2x^2=0[/tex] have 5 roots.
As from the graph, we see that there are 2 real roots of the equation.
So, the other 3 roots must be complex.
Hence, the option C is correct.
