Question

If alpha, beta are the zeroes of the polynomial 2x^2+3x+1,find a polynomial whoes zeros are alpha /beta and beta /alpha

Answer 1

the formula to form a quad eqn is xpower2-(sum of roots) x+product of roots

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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