Form the polynomial whose zeroes are 3 + √3, 3 - √3.

Given: 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) = (3) ² - (√3) ²
= 9 – 3 = 6
The required polynomial is:
x ² - (sum of the zeroes) x + Product of the zeroes ⇒ x ² - (6) x + (6)
∴ x ² - 6x + 6 is the required polynomial.