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

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

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

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

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

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

By distributive property of multiplication

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

**Therefore, (x ^{3} - 2x^{2} - 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 (x^{3} - 2x^{2} - 3x + 6).

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