Question

form the polynomial whose zeroes are 3+√3,3-√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  

Answer 2

$\alpha + \beta = 3 + \sqrt{3} + 3 - \sqrt{3} = 6 \\ \alpha \beta = (3 + \sqrt{3} )(3 - \sqrt{3} ) = 9 - 3 = 6$
${x}^{2} - ( \alpha + \beta )x + \alpha \beta$
x^2-6x+6 Ans