Bunuel wrote:
Which of the following equations has a root in common with \(x^2−6x+8=0\)?
A. \(x^2+x−2=0\)
B. \(x^2+4=0\)
C. \(x^2−12x+16=0\)
D. \(32−2x^2=0\)
E. \(x^2−4x+16=0\)
We can start by factoring the given equation of x^2 - 6x + 8 = 0:
(x - 4)(x - 2) = 0
x = 4 or x = 2
Now let’s analyze each answer choice to determine which has a root in common with x^2 - 6x + 8 = 0.
A) x^2 + x - 2 = 0 (x + 2)(x - 1) = 0
x = -2 or x = 1
Answer choice A DOES NOT have a root in common with x^2 - 6x + 8 = 0.
B) x^2 + 4 = 0 Since x^2 + 4 = 0 cannot be factored (over the real numbers), answer choice B DOES NOT have a root in common with x^2 - 6x + 8 = 0.
C) x^2 - 12x + 16 = 0 Since x^2 - 12x + 16 = 0 cannot be factored (over the integers), answer choice C DOES NOT have a root in common with x^2 - 6x + 8 = 0.
D) 32 - 2x^2 = 02(16 - x^2) = 0
2(4 + x)(4 - x) = 0
x = -4 or x = 4
Answer choice D DOES have a root in common with x^2 - 6x + 8 = 0.
E) x^2 - 4x + 16 = 0Since x^2 - 4x + 16 = 0 cannot be factored (over the real numbers), answer choice E DOES NOT have a root in common with x^2 - 6x + 8 = 0.
Answer: D
_________________
5-star rated online GMAT quant
self study course
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.