SOLUTION: I am studying for a college algebra test and have hit a wall with this question:
Let f(x)= x^3-8x^2+17x-9. Use the factor theorem to find other solutions to
f(x)-f(1)=0, besi
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-> SOLUTION: I am studying for a college algebra test and have hit a wall with this question:
Let f(x)= x^3-8x^2+17x-9. Use the factor theorem to find other solutions to
f(x)-f(1)=0, besi
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Question 128933: I am studying for a college algebra test and have hit a wall with this question:
Let f(x)= x^3-8x^2+17x-9. Use the factor theorem to find other solutions to
f(x)-f(1)=0, besides x=1.
Can you please explain how to solve this question, I am going to college via online and have to teach myself from the book and I have been doing well thus far, but am struggling to understand some questions in the Polynomial and rational function section. Thank you so much for your time and help. It is very much appreciated! Answer by oscargut(2103) (Show Source):
You can put this solution on YOUR website! f(1)=1^3-8(1)^2+17(1)-9=1
f(x)-f(1)=(x^3-8x^2+17x-9)-1=x^3-8x^2+17x-10
let take g(x)= x^3-8x^2+17x-10 so
1 is a root of g(x)
The Factor Theorem. x − r is a factor of a polynomial P(x) if and only if r is a root of P(x).
so you have to do the division of g(x)/(x-1)
1 -8 17 -10
1 1 -7 10
1 -7 10 0
so g(x)=(x-1)(x^2-7x+10)
now you have to solve x^2-7x+10=0 using formula solutions are (7+sqrt(9))/2 and
(7-sqrt(9))/2 so the other roots are 5 and 2
R: x=2 and x=5
