SOLUTION: 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.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 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.      Log On


   

Question 65528: 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.
Answer by venugopalramana(3286) About Me  (Show Source):
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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.
LET G(X) = F(X)-F(1)=X^3-8X^2+17X-9-[1-8+17-9]=0
G(X)=X^3-8X^2+17X-10=0
FACTORS OF 10 ARE + OR - 1,2,5,10
G(2)= 2^3-8*2^2+17*2-10=8-32+34-10=0.........HENCE (X-2) IS A FACTOR
G(5)= 5^3-8*5^2+17*5-10=125-200+85-10=0......HENCE (X-5) IS A FACTOR