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If a and b are roots of the quadratic equation x2 - 4x + 1 = 0, what is a+b?

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If a and b are roots of the quadratic equation x2 - 4x + 1 = 0, what is a+b?

by Max@Math Revolution » Thu May 14, 2020 1:00 am

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[GMAT math practice question]

If a and b are roots of the quadratic equation x^2 - 4x + 1 = 0, what is \(\sqrt{a}+\sqrt{b}\) ?

A. 2 \(\sqrt{2}\)
B. ±2\(\sqrt{2}\)
C. \(\sqrt{6}\)
D. ±\(\sqrt{6}\)
E. ±8
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Re: If a and b are roots of the quadratic equation x2 - 4x + 1 = 0, what is a+b?

by Max@Math Revolution » Sun May 17, 2020 6:27 pm
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We have (x - a)(x - b) = x^2 – (a + b)x + ab = x^2 - 4x + 1. Thus a + b = 4 and ab = 1.
(√a + √b)^2 = (√a + √b)(√a + √b) = a + 2√ab + b = a + b + 2√ab = 4 + 2√1 = 6.
Thus, we have √a + √b = √6 since √a and √b are greater than or equal to 0.

Therefore, C is the answer.
Answer: C
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