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