Question

find a quadratic polynomial whose zeros are one upon two plus two root three and one upon two minus two root three

Answer 1

Given zeroes are ,
1/(2+2√3) and 1/(2-2√3)

sum of the zeroes=1/(2+2√3)+1/(2-2√3)

sum of the zeroes=(2+2√3+2-2√3)/(4-12)

sum of the zeroes=4/-8=-1/2
and,
product of zeroes={1/(2+2√3)}{1/(2-2√3)}

product of zeroes=-1/8

We know that any quadratic polynomial is in the form of,
=k{x²-(sum of zeroes)x+product of zeroes}

=k{x²-(-1/2)x-1/8}
Let k=8
=8x²+4x-1


Hence 8x²+4x-1 is the required quadratic polynomial.