if alpha and bita are the zeros of polynomial p(x=3xsquare+2x+1,find the polynomial whose zeros are 1-alpha/1+alpha and 1-bita/1+bita

Answer 1

for ease of typing I will use a and b instead

for 3x^2 + 2x + 1= 0
the sum of the roots = a+b = -2/3
the product of the roots = ab = 1/3

then (1-a)/(1+a) + (1-b)/(1+v) , (sum of new roots)
= ((1-a)(1+b))/((1+a)(1+b))
= (2 - 2ab)/(1 + a+b + ab)
= (2 - 2(1/3))/(1 - 2/3 + 1/3)
= (4/3)/(2/3) = 2

(1-a)/(a+a) (1-b)/(1+b)
= (1 -a -b + ab)/(1+a+b+ab)
= (1 + 2/3 + 1/3)/(1 -2/3 + 1/3)
= 2/(2/3)
= 3

so new equation is
x^2 - 2x + 3 = 0

check my arithmetic