Which of the following equations has a root (solution) in common with x² - 6x + 5 = 0?
{A} x² + 1 = 0
{B} x² - x - 2 = 0
{C} 2x² - 2 = 0
{D} x² - 2x - 3 = 0
{E} x² - 10x - 5 = 0
Factor x² - 6x + 5 = 0 to get (x - 1)(x - 5) = 0
So, the roots are x =
1 and
5
At this point, we aren't necessarily required to solve each equation. We can simply plug one of the roots into each of the five equations and see if it works.
Since it's pretty easy to plug a 1 into an equation, let's plug
x = 1 into the answer choices.
{A} x² + 1 = 0: we get
1² + 1 =
2 [nope, we wanted 0]
{B} x² - x - 2 = 0: we get
1² -
1 - 2 =
-2 [nope, we wanted 0]
{C} 2x² - 2 = 0: we get 2(
1)² - 2 =
0 perfect!!
STOP
So, x =
1 is a solution to the equation in answer choice
C, so this is the correct answer.
Cheers,
Brent
)
