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

x^{3} - 2x^{2} - 3x + 6

x^{3} + 2x^{2} - 3x - 6

x^{3} - 3x^{2} - 5x + 15

x^{3} + 3x^{2} - 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 a^{2} - b^{2} = (a + b)(a - b)

y = (x^{2} - 5)(x + 3)

By further calculation,

y = x^{3} + 3x^{2} - 5x - 15

Therefore, the polynomial is x^{3} + 3x^{2} - 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 x^{3} + 3x^{2} - 5x - 15.

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