Question

Find a quadratic polynomial whose zeroes are 3+root 2 and 3-root 2

Answer 1

Hi friend,
Any quadratic polynomial whose roots are α and β will be of the form 
x²-x(α+β)+αβ so here α=3+√2 ,β=3-√2 so polynomial is x²-(3+√2+3-√2)+(3+√2)(3√-√2)=x²-6x+7.

Answer 2

let α and β two zeroes of the polynomial
given α = 3+√2 
β= 3-√2

i) sum of the zeroes = α+β =3+√2 +3-√2 = 6

ii) product of the zeroes = αβ = (3+√2) (3 -√2)
 = (3)² - (√2)²
= 9 -2
=7

required polynomial
= x² - (α+β)x +αβ
= x² -6x +7