Question

find the quadratic poly whose roots are 3+√3 and 3-√3​

Answer 1

The zeroes are 3 + √3 and 3 - √3. ∴ Sum of the zeroes = ( 3 + √3) + ( 3 - √3) = 6

∴ Product of the zeroes = ( 3 + √3) ( 3 - √3) = 9 - (√3)2

= 9 - 3 = 6

The required polynomial is

x2 - (sum of the zeroes) x + Product of the zeroes ⇒ x2 - (6)x + 6

∴ x2 - 6x + 6