Which of the following is a polynomial with roots: -square root of 3, square root of 3, and 2?
x³ - 2x² - 3x + 6
x³ - 3x² - 5x + 15
x³ + 2x² - 3x - 6
x³ + 3x² - 5x - 15

Solution:

Given:

Roots are -√3, √3 and 2

y = (x - (-√3))(x - √3)(x - 2)

By further calculation

y = (x + √3)(x - √3)(x - 2)

From the algebraic identity (a² - b²) = (a + b)(a - b)

y = (x² - 3)(x - 2)

By distributive property of multiplication

y = x³ - 2x² - 3x + 6

Therefore, (x³ - 2x² - 3x + 6) is a polynomial with roots square root of 3, square root of 3, and 2.

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

Summary:

The polynomial with roots square root of 3, square root of 3, and 2 is (x³ - 2x² - 3x + 6).