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

YEEEEEET Dec 28, 2018

#1**+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

CPhill Dec 28, 2018