SOLUTION: How do you create a quadratic equation if you only have the solutions? I am really not getting the quadratic equation math at all. Example if I have theses two numbers, 8 and 4/5 a

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: How do you create a quadratic equation if you only have the solutions? I am really not getting the quadratic equation math at all. Example if I have theses two numbers, 8 and 4/5 a      Log On


   

Question 465444: How do you create a quadratic equation if you only have the solutions? I am really not getting the quadratic equation math at all. Example if I have theses two numbers, 8 and 4/5 as solutions to create a quadratice equation.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
A quadratic equation is one in which the
highest power of x is 2.
This will automatically happen when you
multiply something like +%28x+%2B+2%29%2A%28x+-7%29+
You get +x%5E2+-+5x+-+14+
---------------------
Now suppose you have 2 solutions to a
quadratic equation,
(1) +x+=+8+
(2) +x+=+4%2F5+
-----------
Subtract 8 from both sides of (1)
(1) +x+-+8+=+0+
Subtract +4%2F5 from both sides of (2)
(2) +x+-+4%2F5+=+0+
----------------
The key now is that if you multiply (1) and (2),
you will have +0%2A0+=+0, so
+%28x-8%29%2A%28x-4%2F5%29+=+0+
Now do the multiplication
+x%5E2+-+8x+-+%284%2F5%29%2Ax+%2B+32%2F5+=+0+
Multiply both sides by 5
+5x%5E2+-+40x+-+4x+%2B+32+=+0+
+5x%5E2+-+44x+%2B+32+=+0+ answer
--------------------
Now you can check the answer
Does +x+=+4%2F5+ work?
+5%2A%284%2F5%29%5E2+-+44%2A%284%2F5%29+%2B+32+=+0+
+5%2A%2816%2F25%29+-+44%2A%2820%2F25%29+%2B+32+=+0+
Multiply both sides by +25+
+80+-+880+%2B+800+=+0+
+880+-+880+=+0+
+0+=+0+
OK
You can check the other solution