Question

Can someone tell me if I'm on the right path and help me do this?

Answer 1

Using the fundamental theorem of algebra, complete the following:
1.Determine how many, what type, and find the roots for f(x) = x^4 + 21x^2 – 100.
Factor
(x^2 + 25) • (x + 2) • (x - 2)
x^2 + 25 = 0
x^2 = -25 (complex root)
Square both sides
x = Square root of -25
x = 5i
x = -2 (normal root)
x = 2 (normal root)
2.Determine how many, what type, and find the roots for f(x) = x^3 - 5x^2 – 25x + 125.
(x + 5) • (x - 5) ...? how do you factor this?

Answer 2

how does your material define the fun thrm of algebra?

Answer 3

Complex root is supposed to be next to 5i
Sorry.
"The fundamental theorem of algebra states that for any polynomial of degree n, the polynomial has n total roots—both real and complex."

Answer 4

then it really only helps define the number of roots, the type and what they are ahv eno bearing on it

Answer 5

and for the 2nd one, try grouping since they all seem to have 5 as a common factor

Answer 6

x^3 - 5x^2 – 25x + 125

( x^3 - 5x^2) – (25x -125)

x^2(x - 5) – 25(x -5)

Answer 7

Oh ok that makes more sense

Answer 8

How do you find the roots of the second one?

Answer 9

same way as you did the first one:

(x^2-25)(x-5)=0

(x+5)(x-5)(x-5) = 0

Answer 10

Thanks a lot :)