Which of the following equations has a root in common with

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

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

Solution:

Notice that x^2 - 6x + 5 can be factored as (x - 5)(x - 1); therefore the roots of the equation (x - 5)(x - 1) are x = 5 and x = 1.

To determine which of the given equations has x = 1 or x = 5 as one of its roots, we will substitute x = 1 and x = 5 into all the equations. Let’s start with x = 1:

A) 1^2 + 1 ≟ 0 No!

B) 1^2 - 1 - 2 ≟ 0 No!

C) 2(1)^2 - 2 ≟ 0 Yes!

Answer: C