Form the polynomial whose zeroes are 3 + √3 , 3 – √3.
Answers:
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