Question

If
x^2+ x − 2 = (x − a) (x − b),
determine the value of (a − b)^2

Answer 1

You're trying to factor the equation x^2 +x -2. To factor this into (x-a)(x-b) you need to find two numbers that multiply to get -2 and add to get +1. With a little trial and error you'll find the values are -1 and +2. So, let a=-1 and b=+2. If you'd like, you can multiply (x+1)(x-2) to confirm it equals the original equation.

Now, we just plug in and solve:
(a-b)^2
(-1-2)^2
(-3)^2
9

So your answer is 9.

Answer 2

@vinnv226 i appreciate your help but that was my original answer and it was incorrect so now i'm even more confused :(

Answer 3

Maybe there is a typo ? if they got the signs wrong, maybe they want 1 as the answer. But as written, 9 is the answer

Answer 4

@phi and @vinnv226 the options are 46,16,25, and 9. I already tried 9 and it marked it wrong.

Answer 5

In that case, the question is bogus. make a copy of it and the answers, and show your teacher.

Answer 6

as written,
x^2+ x − 2
factors into
(x - 1) (x - -2)
a= 1, b= -2
a - b is 1 - -2 = 1+2= 3
3^2 = 9

if you swap a and b you get -3, and -3*-3 is also 9.

Answer 7

are your sure you didn't type something other than 9 ?

Answer 8

Its in ABC answer choice and that was my original math and my answer choice was 9. I will consult my teacher thank you (: @phi