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19 Nov 2020, 03:48
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What is the value of a + b?
(1) ‘a’ and ‘b’ are the roots of the equation x^3 – 3x^2 + 5x – 9 = 0.
(2) ‘a’ and ‘b’ are the roots of the equation x^3 + 9x^2 + 27x + 27 = 0.
need help
(1) ‘a’ and ‘b’ are the roots of the equation x^3 – 3x^2 + 5x – 9 = 0.
(2) ‘a’ and ‘b’ are the roots of the equation x^3 + 9x^2 + 27x + 27 = 0.
need help
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19 Nov 2020, 07:18
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This question makes absolutely no sense. The cubic in Statement 1 does not have two real roots. It has one real root, and two different roots that are both imaginary numbers. So I don't even know what Statement 1 could even mean -- if you only consider real numbers, as you are meant to do on the GMAT, there is only one root. Statement 1 claims there are two. If you include complex numbers, there are three roots. Statement 1 simply cannot be true.
Similarly, the cubic in Statement 2 is equal to (x + 3)^3, so it only has a single root. So Statement 2 doesn't make sense either. Not only that, but the real root in Statement 1 is different from the real root in Statement 2, so the two Statements cannot both be true, which can never happen in a real GMAT question.
You also don't need to know anything about nontrivial cubics for the GMAT, so the question is beyond the scope of the test, but that's honestly the least of its problems.
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