Question

If alpha and beta are the roots of quad. Polynomial 4x²+4x+1, then form a quad. Polynomial whose zeros are 2 alpha and 2 beta.

Answer 1

given equation is 4 x square+4x+1
the zeros of this are alpha and beta

now,
4x square+2x+2x+1
2x(2x+1)+1(2x+1)
(2x+1)(2x+1)
so,
2x=1
x=1/2
the Alpha is =1/2
the 2 Alpha =1

the beta = 1/2
the 2beta = 1

the sum of 2 alpha and 2 beta = 2

the product of 2 alpha and 2 Beta is 1


if alpha and beta are roots of a quadratic polynomial then P(X )=x square - the( sum of the zeros ) + product of zeros

the quadratic polynomial whose zeros are 2 alpha and 2beta is a x square - 2x +1
I hope it is helpful for you