Answer :

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.

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