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

x3 − 2x2 − 3x + 6
x3 + 2x2 − 3x − 6
x3 − 3x2 − 5x + 15
x3 + 3x2 − 5x − 15

It's the first one. The way you figure that out is to turn each one of those roots into a factor of the polynomial, like this: if a root is 2, the factor is (x - 2). The factors of this polynomial are (x + sqrt(3)), (x - sqrt(3)), and (x - 2). When you multiply all of those together by FOILing, you get the first choice.

=

Step-by-step explanation: Given roots of the polynomial

Therefore, factors of the polynomial with given roots would be

.

Multiplying those factors.

.

Therefore, correct option is first option x^3-2x^2-3x+6.

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