SOLUTION: Ok, I'm going to try this one more time... I need help solving AND factoring the following equation (taken from Bittinger's College Algebra: Graphs and Models 4th Edition, page

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Question 215713: Ok, I'm going to try this one more time...
I need help solving AND factoring the following equation (taken from Bittinger's College Algebra: Graphs and Models 4th Edition, page 76, problem number 39.)

A point to remember: The x^2 is NEGATIVE, and the 2x and 3 are both POSITIVE.
Thank you in advance!
Found 2 solutions by nerdybill, drj:
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
Answer by drj(1380)   (Show Source): You can put this solution on YOUR website!


Step 1. Let's factor out negative 1 so now we have

Step 2. We need two integers m and n such that their sum is -2=m+n and their product mn=-3.

Step 3. The integers are -3 and 1. Then,

Step 4. ANSWER: y = -x^2 + 2x + 3=-1*(x-3)(x+1) when y=0 we are finding x as solutions where it intersects the x-axis or in our case (x-3)=0 and (x+1)=0 or x=3 and x=-1.

You can also use the quadratic formula given as

where a=-1, b=2 and c=3.

The graph is shown below:

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=16 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: -1, 3. Here's your graph:



I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
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