Question

If alpha and beta are the zeroes of a polynomial 3x²+2x+1 . Find the polynomial whose zeroes are 1-alpha/1+alpha and1-beta/1+beta​

Answer 1

Answer:

f(x) = 3x²+2x+1

roots are a and b

new zeroes 1-a/1+a   and 1-b/1+b

trick :  x = 1-a/1+a

          x + xa = 1-a

           x+ xa - 1 +a = 0

       a(x+1) = 1-x

      a = 1-x/1+x

now replace x by 1-x/1+x in f(x)

3 (1-x/1+x)² + 2(1-x/1+x) + 1 = 0

x² -2x +3 =0 is the required polynomial.

hope my ans is correct.

Step-by-step explanation:

Hope it helps