SOLUTION: Three roots of a fourth-degree polynomial equation with rational coefficients are 5+√3, �17, and 2-√4. Which number also is a root of the equation? A. 17 B. 2+√

Question 986181: Three roots of a fourth-degree polynomial equation with rational coefficients are 5+√3, �17, and 2-√4. Which number also is a root of the equation?
A. 17
B. 2+√4
C. 4-√2
D. 5-√3
How does this make sense? I thought that if you switched the addition/subtraction symbol, then you will have the other root. So shouldn't A, B, and D all be correct?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since , we know that . They made this root a bit more complicated than it had to be to confuse you. The three roots, as simple as they can get, are given as , , and

Rule: if you have a polynomial with rational coefficients, and you have a root , then must also be a root as well.

So if is a root, then must also be a root (note: a = 5, b = 1, c = 3 in this case)

Final Answer: Choice D)
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SOLUTION: Three roots of a fourth-degree polynomial equation with rational coefficients are 5+&#8730;3, �17, and 2-&#8730;4. Which number also is a root of the equation? A. 17 B. 2+&#8730;

SOLUTION: Three roots of a fourth-degree polynomial equation with rational coefficients are 5+√3, �17, and 2-√4. Which number also is a root of the equation? A. 17 B. 2+√