Question

Write a polynomial that has the give numbers as roots-3, 2 +sqrt3

Answer 1

Given roots are (-3) and (
`2 + √(3)`)

`2 + √(3)` is one of the root. So other root is
`2 - √(3)`

So we have three roots -3 ,
`2 + √(3)` and
`2 - √(3)`

Now we write the all the roots in factor form

`(x -(-3)) (x- (2 + √(3)) (x- (2 - √(3))`

`(x + 3) (x- 2 - √(3)) (x- 2 + √(3))`

Now we multiply last two parenthesis

`(x + 3) (x^2- 2x +x√(3) -2x + 4 -2√(3) - x √(3) +2 √(3) - 3)`

Now combine like terms

`(x + 3) (x^2- 4x+1)`

`(x^3 -4x^2 +x + 3x^2-12x +3)`

`(x^3 - x^2 - 11x +3)`