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5 votes
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

User Pepedou
by
8.4k points

2 Answers

5 votes

Answer:=
x^3-2x^2-3x+6.


Step-by-step explanation: Given roots of the polynomial
-√(3) , √(3) , 2.

Therefore, factors of the polynomial with given roots would be


(x-√(3)), (x+√(3)), (x-2).

Multiplying those factors.


(x-√(3))(x+√(3))(x-2).


\mathrm{Expand}\:\left(x-√(3)\right)\left(x+√(3)\right)=x^2-\left(√(3)\right)^2


=x^2-3


\left(x-√(3)\right)\left(x+√(3)\right)\left(x-2\right)=\left(x^2-3\right)\left(x-2\right)


\mathrm{Expand}\:\left(x^2-3\right)\left(x-2\right)


=x^3-2x^2-3x+3\cdot \:2


=x^3-2x^2-3x+6

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

User Raj Chaurasia
by
7.4k points
4 votes
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.
User Inaz
by
7.9k points

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