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Let P(x) = 2x³ + a x² + b x + c with a, b, c integers. Given P(sqrt(3)) = 10 - 2 sqrt(3), find the value of 3a + c.

1. 0
2. 4
3. -2
4. 10

Correct answer: 10

Solution

Plug in sqrt(3), group integer terms and sqrt(3) terms, then equate to 10 - 2 sqrt(3). The rational equation gives 3a + c = 10.

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