Question

if alpha and beta are the zeroes of the polynomial x^2-3x-2 find the polynomial whose zeroes are 1÷alpha +beta and 1÷2beta + alpha​

Answer 1

Given:--

x^2-3x-2 is a polynomial with alpha & beta as Roots.

Therefore,

x=-(b)+[(b^2-4ac)^1/2]/2a

i.e,w which gives

alpha=[3+(17)^1/2]/2

& beta=[3-(17)^1/2]/2

now,

alpha+beta=3

& 2x beta+ alpha=3

Therefore,

{1/[alpha+beta]}={1/[2x beta+ alpha]}=1/3

Therefore,

the required polynomial is-- (x-1/3)^2 or

9x^2-6x+1.