Find a quadratic equation whose roots are 3-√(3) and 3 +√(3)

Question

Find a quadratic equation whose roots are
3-
`√(3) and 3 +√(3)`

Answer 1

x² - 6x + 6 = 0

Explanation:

Given the roots are x = 3 -
`√(3)` and x = 3 +
`√(3)` , then the corresponding factors are

(x - (3 -
`√(3)` ) ) and (x - (3 +
`√(3)` ) ), that is

(x - 3 +
`√(3)` ) and (x - 3 -
`√(3)` )

The equation is then the product of the factors

(x - 3 +
`√(3)` )(x - 3 -
`√(3)` ) = 0

(x - 3)² - (
`√(3)` )² = 0

x² - 6x + 9 - 3 = 0

x² - 6x + 6 = 0