-
AbeNeedsAnswers
- Master | Next Rank: 500 Posts
- Posts: 394
- Joined: Sun Jul 02, 2017 10:59 am
- Thanked: 1 times
- Followed by:5 members
We see that one of the roots is (1 + √2), which is not a whole number or it is an irrational root, thus the other root of the quadratic equation must be the conjugate of (1 + √2) = (1 - √2).AbeNeedsAnswers wrote: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
D
To get the conjugate, reverse the sign of the irrational part. Since in the given root, (1 + √2), the sign of the irrational part is +, so we must make it - to get its conjugate.
Thus, the two roots are: (1 + √2) and (1 - √2)
You must know that any quadratic equation can be written as:
x^2 - (Sum of the roots)*x + (Product of the roots) = 0
For the given roots,
Sum of the roots = (1 + √2) + (1 - √2) = 2, and
Product of the roots = (1 + √2) x (1 - √2) = 1^2 - (√2)^2 = 1 - 2 = -1
Thus, the quadratic equation is x^2 - (2)*x + (-1) = 0
[spoiler]x^2 - 2x -1 = 0[/spoiler]
The correct answer: D
Hope this helps!
Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide
-Jay
_________________
Manhattan Review GMAT Prep
Locations: New York | Bangkok | Abu Dhabi | Rome | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
