Question

find a quadratic polynomial whose zeros are (3+√2) and (3-√2)

Answer 1

let the sum of zeroes be (3-√2 )
product of zeroes be (3+√2)
the polynomial be
x^2-x(sum of zeroes )+product of zeroes
x^2-x(3+√2)+(3-√2)

Answer 2

alpha = 3+✓2 , Beta = 3-✓2.

Alpha + Beta = 3+✓2+3-✓2 = 6

Alpha × Beta = (3+✓2)(3-✓2) = (3)²+(✓2)²-2× 3 × ✓2.
= 9 + 2-6✓2 = 11-6✓2...

REQUIRED POLYNOMIAL = X²-(Alpha+ Beta) X+ Alpha × Beta