Question

LOOK AT PIC BELOW THX

Answer 1

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.

Explanation:

We are given the equation
`x^5=-2x^2` i.e.
`x^5+2x^2=0`.

So, we have a polynomial
`x^5+2x^2` of degree 5.

Fundamental Theorem of Algebra states that 'An n-degree polynomial have 'n' number of roots'.

Thus, the equation
`x^5+2x^2=0` 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.