Question

IF ALPHA AND BETA ARE THE ZEROS OF POLYNOMIAL 3X2+2X+1, FIND THE POLNOMIAL WHOSE ZEROS ARE [ 1- ALPHA] / [1+ ALPHA] AND [1-BETA] / [1+ BETA].

Answer 1

In this picture I've added both zeroes and found the value of (alpha+beta)

Similarly you have to do by multiplying the zeroes and then find the another value.

And at last, put the values in the equation given below:-

${x}^{2} - x( \alpha + \beta ) + \alpha \beta$

Answer 2

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.

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@GauravSaxena01