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Which of the following is a polynomial with roots: − square root of 3 , square root of 3, and −2? (6 points) Question 7 options: 1) x3 − 2x2 − 3x + 6 2) x3 − 3x2 − 5x + 15 3) x3 + 2x2 − 3x − 6 4) x3 + 3x2 − 5x − 15

User Tapas Jena
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1 Answer

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Answer:

The polynomial is
x^(3) - 1.46x^(2) - 3.93x + 6

Explanation:

A nth order polynomial f(x) has roots
x_(1), x_(2), ..., x_(n) such that
f(x) = (x - x_(1))*(x - x_(2))*...*(x - x_(n)},

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

So


x_(1) = x_(2) = √(3)


x_(3) = -2

Then


(x - √(3))^(2)*(x - (-2)) = (x - √(3))^(2)*(x + 2) = (x^(2) -2x√(3) + 3)*(x + 2) = x^(3) + 2x^(2) - 2x^(2)√(3) - 4x√(3) + 3x + 6

Since
√(3) = 1.73


x^(3) + 2x^(2) - 3.46x^(2) - 6.93x + 3x + 6 = x^(3) - 1.46x^(2) - 3.93x + 6

The polynomial is
x^(3) - 1.46x^(2) - 3.93x + 6

User Damkulul
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