Which of the following equations has a root in common with...

[AAPL]

Official Guide

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

OA C

[Brent@GMATPrepNow]

Official Guide

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

OA C

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

[swerve]

Official Guide

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

OA C

\(x^2 - 6x + 5 = 0\)
\((x-5)(x-1) = 0\)
The roots are \(1\) and \(5\)

We need to check for each option to calculate the roots. This can be done by plugging in the values in the equations

A. \(x^2 + 1 = 0\). None of 1 or 5 satisfies this equation

B. \(x^2 - x - 2 =0\). None of 1 or 5 satisfies this equation

C. \(2x^2 - 2 =0. x = 1\) satisfies this equation. Hence this has a common root

D. \(x^2 - 2x - 3 =0\). None of \(1\) or \(5\) satisfies this equation

E. \(x^2 - 10x - 5 = 0\). None of \(1\) or \(5\) satisfies this equation

Therefore, C

[Scott@TargetTestPrep]

Official Guide

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

OA C

First, let’s solve x^2 - 6x + 5 = 0 by factoring:

(x - 5)(x - 1) = 0

x = 5 or x = 1

We can solve the equations in the given choices by factoring also. However, we see that the equation in choice A is not factorable (the equation is a sum of squares), so we can start with choice B.

B. (x - 2)(x + 1) = 0

x = 2 or x = -1

We see that the equation in choice B does not have a root in common with x^2 - 6x + 5 = 0.

C. 2(x^2 - 1) = 0
2(x - 1)(x + 1) = 0

x = 1 or x = -1

We see that the equation in choice C does have a root in common with x^2 - 6x + 5 = 0 (namely, x = 1).

Answer: C