Gmat_mission wrote: ↑Thu May 21, 2020 1:30 am
Which of the following equations has a root in common with \(x^2−6x+5=0?\)
A. \(x^2+1=0\)
B. \(x^2−x−2=0\)
C. \(2x^2−2=0\)
D. \(x^2−2x−3=0\)
E. \(x^2−10x−5=0\)
[spoiler]OA=C[/spoiler]
Source: Official Guide
Step 1: Solve the given equation: x² – 6x + 5 = 0
This is a quadratic set equal to zero, so let's factor to get:
(x-1)(x-5)=0
So, we have two solutions (roots):
x=1 or
x=5
Step 2: Solve the other 5 equations to see which one has a root (solution) of x=1 or x=5
IMPORTANT: It appears that the only way to answer this question is to keep checking every single answer choice until we find that one that has a solution of either x=1 or x=5. Given this, where do you think the test-maker would hide the correct answer? In these situations, I always start at E and work my way up. Is the answer to these questions always E (or perhaps D)? No, but it's more likely that the correct answer is near the bottom.
Okay, E: x² – 2x – 3 =0
Factor to get: (x-3)(x+1)=0
So, x=3 or x=-1
No shared solutions (roots) so keep going.
D: x² – 2x -3 =0
Factor: (x - 3)(x + 1) = 0
So, x = 3 or x = -1
No shared solutions (roots) so keep going.
C: 2x² – 2 =0
Factor: 2(x² - 1) = 0
Keep factoring: 2(x+1)(x-1)=0
So,
x=1 or x=-1
We have a common solution, so the correct answer must be C
Cheers,
Brent
