Question

Fundamental Theorem of Algebra...

(x+7)^5
1. Using the Fundamental Theorem of Algebra explain how many roots your expression can have. How many real roots and how many complex roots are possible?

Answer 1

A real root of fifth-grade multiplicity/No complex roots.

Explanation:

The Fundamental Theorem of Algebra states that every polynomial with real coefficients and a grade greater than zero has at least a real root. Let be
`f(x) = (x+7)^(5)`, if such expression is equalized to zero and handled algebraically:

1)
`(x+7)^(5) = 0` Given.

2)
`(x+7)\cdot (x+7)\cdot (x+7)\cdot (x+7)\cdot (x+7) = 0` Definition of power.

3)
`x+7=0` Given.

4)
`x = -7` Compatibility with the addition/Existence of the additive inverse/Modulative property/Result.

This expression has a real root of fifth-grade multiplicity. No complex roots.