Which of the following equations has 1 + √2 ​as PS05888

GMAT PS05888

Which of the following equations has 1 + √2 as one of its roots?

A. x^2 + 2x − 1 = 0
B. x^2 − 2x + 1 = 0
C. x^2 + 2x + 1 = 0
D. x^2 − 2x − 1 = 0
E. x^2 − x − 1 = 0

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[rezamorovati]

The penny dropped!! Thank you so much!!

[Ntoh]

Thank you so much for your videos. I just discovered your channel recently and your explanations are really helpful.

I’m just confused about what you refer to in 0:43, when you mention that the correct answer choice will need to have something that “subtracts out” a 3 or 2root2? What is this process related to?

I solved the question based using knowledge of the Quadratic Formula and working backwards to infer what a, b and c would need to be with regards to their values and signs to give me a term with positive 1 and a positive value of 2 under the square root. From a process of mental substitution, I could see that D was the only option that worked. Unfortunately this process took more than 2 minutes to complete, so I’d like to understand your approach since it seemed way quicker to reach the correct answer.

[aricoleman]

I just set it equal to x. Didn’t quite understand this method