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avatar+622 

 for this question i did conjugate of 1/x = x/1 which is just x 

subbed in x gave me the original which is x^3 - 5x -1 =0 

however i was told the answer should be x^3 + 5x^2 -1 = 0

please help thanks

 Dec 28, 2018
 #1
avatar+94453 
+1

(x - 1/A) (x - 1/B) (x - 1/C) = 0

 

(AX - 1) (BX - 1) (Cx - 1) / (ABC) = 0

 

(Ax - 1) (Bx - 1) (Cx - 1) = 0

 

[ (ABx^2 - (A + B)x  + 1 ] [ Cx - 1 ] = 0

 

(ABC)x^3 - (AC + BC)x^2 + Cx - ABx^2 + (A + B)x - 1 = 0

 

(ABC)x^3 - (AC + BC + AB)x^2 +(A + B + C)x  - 1 = 0

 

Write the original polynomial as    x^3 + 0x^2 - 5x - 1  =  ax^3 + bx^2 +cx + d

 

a = 1    b = 0    c = -5     d = - 1

 

Adding the original roots in the original polynomial = (A + B + C) =   -b/a  = -0/ 1   = 0

 

Multiplying the roots gives (ABC) =  -d /a =   - (-1) /1  = 1

 

And (AC + BC + AB) =  c/a    = -5 /1 = - 5

 

So

 

The new polynomial is

 

(1) x^3  - (- 5)x^2   - 1   =

 

x^3 + 5x^2 - 1

 

 

cool cool cool

 Dec 28, 2018
edited by CPhill  Dec 28, 2018
 #2
avatar+622 
+1

thank you

YEEEEEET  Dec 29, 2018

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