SOLUTION: f(x)= 2x^2-16x+30 g(x)= x*(x-3)^2*(x+1)^4 Find the zeros of g(x) and f(x).

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Question 1009152: f(x)= 2x^2-16x+30
g(x)= x*(x-3)^2*(x+1)^4
Find the zeros of g(x) and f(x).
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
set f(x) equal to 0 and you get:

2x^2 - 16x + 30 = 0

factor out a 2 and you get:

2 * (x^2 - 8x + 15) = 0

factor x^2 - 8x + 15 to get:

2 * (x-3) * (x-5) = 0

set each of these factors equal to 0 to get:

x-3 = 0 and x-5 = 0

solve for x to get x = 3 and x = 5.

the zeroes of y = 2x^2 - 16x + 30 are at x = 3 and x = 5.

here's the graph:

$$$

your second equation is:

g(x)= x(x-3)^2 (x+1)^4

set g(x) equal to 0 and you get:

x * (x-3)^2 * (x+1)^4 = 0

set each of these factors equal to 0 and you get:

x = 0 and (x-3)^2 = 0 and (x+1)^4 = 0

solve for x in each of these equations to get:

x = 0

(x-3)^2 = 0
take square root of both sides of this equation to get:
(x-3) = 0
solve for x to get x = 3

(x+1)^4 = 0
take the fourth root of both sides of this equation to get:
x + 1 = 0
solve for x to get x = -1

your zeroes are at x = -1, x = 0, and x = 3

here's the graph:

$$$