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

Solution:

Given: -square root of 5, square root of 5, and -3

If a polynomial contains root b, then (x - b) is the factor of a polynomial.

It can be written as

-√5, √5 and -3

y = (x - (-√5)) (x - √5) (x + 3)

y = (x + √5)(x - √5)(x + 3)

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

y = (x² - 5)(x + 3)

By further calculation,

y = x³ + 3x² - 5x - 15

Therefore, the polynomial is x³ + 3x² - 5x - 15.

Which of the following is a polynomial with roots: -square root of 5, square root of 5, and -3?

Summary:

The polynomial with roots -square root of 5, square root of 5, and -3 is x³ + 3x² - 5x - 15.