Question

find the quadratic polynomial whose zeros are 3+root 2/3-root2 and 3-root2/3+root 2

Answer 1

i hope this will useful to u

Answer 2

it has a specific formula,...
x^2-sum of the rootsx+product of the roots.
so,...
sum of the roots =(3+√2/3-√2)+(3-√2/3+√2)
= (3+√2)(3+√2)+(3-√2)(3-√2)/(3-√2)(3+√2).
= (3+√2)^2+(3-√2)^2/(3)^2-(√2)^2.
= [(3)^2+2x3x√2+(√2)^2]+{(3)^2-2x3x√2+(√2)^2]/9-2.
= (11+6√2)+(11-6√2)/7.
= 22/7.
now, product of the roots...
(3+√2/3-√2)(3-√2/3+√2)
= 1.
now putting in formula...,
x^2-22/7x+1.
= 7x^2-22x+7.
so, the quadratic equation is,
7x^2-22x+7.
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