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Sagot :
The function [tex]f(x)=x^3 - 8x^2 + 42[/tex] contains zeros located at 7, –2, 3.
where the other two zeros exist X = 5, and x = -2.
How to determine the zeros of the function
[tex]f(x)=x^3 - 8x^2 + 42[/tex]?
Given: [tex]f(x)=x^3 - 8x^2 + 42[/tex]
To turn roots into factors and then multiply then you have
[tex]f(x) = a(x + 2)(x -5)^2[/tex]
[tex]f(x) = a(x + 2)(x^2 - 10x + 25)[/tex]
[tex]f(x) = a(x^3 - 8x^2 + 5x + 50)[/tex]
By using synthetical or the factor theorem,
f(-2) = a(-8 - 8(4) + 5(-2) + 50) = a(0) = 0.
f = -2
€(5) = a(125 - 8(25) + 5(5) + 50) = a(0) = 0
f = 5 works
Divide it into the second multiplying
And you should get [tex]$x^2 - 3x - 10 = (x - 5)(x + 2)[/tex],
where the other two zeros exist X = 5, and x = -2.
To learn more about factors refer to:
https://brainly.com/question/11930302
#SPJ4
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