Question

Which of the following is a polynomial with roots: − square root of 3 , square root of 3, and −2? (6 points) Question 7 options: 1) x3 − 2x2 − 3x + 6 2) x3 − 3x2 − 5x + 15 3) x3 + 2x2 − 3x − 6 4) x3 + 3x2 − 5x − 15

Answer 1

The polynomial is
`x^(3) - 1.46x^(2) - 3.93x + 6`

Explanation:

A nth order polynomial f(x) has roots
`x_(1), x_(2), ..., x_(n)` such that
`f(x) = (x - x_(1))*(x - x_(2))*...*(x - x_(n)}`,

Which of the following is a polynomial with roots: − square root of 3 , square root of 3, and −2?

So

`x_(1) = x_(2) = √(3)`

`x_(3) = -2`

Then

`(x - √(3))^(2)*(x - (-2)) = (x - √(3))^(2)*(x + 2) = (x^(2) -2x√(3) + 3)*(x + 2) = x^(3) + 2x^(2) - 2x^(2)√(3) - 4x√(3) + 3x + 6`

Since
`√(3) = 1.73`

`x^(3) + 2x^(2) - 3.46x^(2) - 6.93x + 3x + 6 = x^(3) - 1.46x^(2) - 3.93x + 6`

The polynomial is
`x^(3) - 1.46x^(2) - 3.93x + 6`