Question 1184612: solve the quadratic equation below using the appropriate method. Show your work or solution.
x ^ 2 - 2x - 8 = 0 Found 2 solutions by Theo, greenestamps:Answer by Theo(13342) (Show Source):
The reference provided by the other tutor is, in my opinion, not a particularly good one. It shows SOLVING several example quadratic equations; but it doesn't provide much explanation on HOW TO SOLVE them.
The instructions for this problem say to solve using "the appropriate method".
It is unclear what "the appropriate" method is; different students will use different methods.
You can ALWAYS solve a quadratic equation using the quadratic formula. However, the probable intent of this problem is to provide practice in solving by factoring.
So let's take a look at what is involved in solving by factoring.
We want to factor x^2-2x-8 into the form (x+a)(x+b) where a and b are integers.
We see that our two numbers a and b have to be such that
(1) their sum a+b is -2; and
(2) their product ab is -8
Clearly the product ab=-8 means one of the numbers is positive and one negative. Then playing around with possible values of a and b to give a product of -8 and a sum of -2 gives us -4 and 2 as the two numbers. So the factorization is
