Question

If α and β are the zeroes of the quadratic polynomial p(x) = x²– x – 2, find a polynomial whose zeroes
are 2α + 1 and 2β + 1.

Answer 1

Sum = α + β =--1/1=1
product = α * β = - 2/1=-2
now
sum of other zeroes = 2α + 1 + 2β + 1
=2( α+ β ) + 2
= 2 * 1+ 2
= 4
product = (2α + 1) ( 2β +1)
=2(α + β) + 4αβ + 1
= 2*1+ 4* - 2+ 1
= - 5
then g (x) = x² - 4x - 5
This is required polynomial with roots 2a(alpha)+1,2b(beta)+1