Question

Determine how many, what type, and find the roots for f(x) = x^3 - 5x^2 – 25x + 125.

Answer 1

using the fundamental theorem of algebra - will medal

Answer 2

Factor x^3 - 5x^2 – 25x + 125 by grouping as follows:
(x^3 - 5x^2) – (25x - 125)

Answer 3

ok, and then I find the gcf's?

Answer 4

Yes. GCF of x^3 and -5x^2. Then GCF of -25x and +125.

Answer 5

ok so that'll be x^2(x-5) and 25(x+5) ?

Answer 6

x^2(x-5) and -25(x-5)

Answer 7

oh ok. since the second part is negative, do I add the two?

Answer 8

f(x) = x^3 - 5x^2 – 25x + 125 = x^2(x - 5) - 25(x - 5) = (x^2 - 25)(x - 5) =
(x + 5)(x - 5)(x - 5) = (x + 5)(x - 5)^2

Answer 9

To find the root, set f(x) = 0 and solve for x.
(x+5)(x-5)^2 = 0 implies x = -5 or x = 5.
The roots are: -5 and 5 (with multiplicity of 2).

Answer 10

ok, thank you! :)

Answer 11

You are welcome.
How many roots? Two
What type of roots? Two real roots
Find the roots: -5 and 5. 5 has a multiplicity of two.