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

Answer:

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

Step-by-step 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.