Find Quadratic Equation From Roots

Date: 9/15/96 at 16:36:41
From: Anonymous
Subject: Find Quadratic Equation From Roots

Write a quadratic equation with roots: -4 +/- sqrt(10)
  
I figured out the sums by adding the two roots.  I got -8 , which is 
right, but I can't figure out how to get the product.  The answer 
should be 6.

Date: 9/16/96 at 1:7:6
From: Doctor Pete
Subject: Re: Find Quadratic Equation From Roots

Okay, you know what the two roots are:

     p = -4 + Sqrt[10]
     q = -4 - Sqrt[10]

and we want to find

     pq = (-4+Sqrt[10])(-4-Sqrt[10]).

Now, here's a hint:

     (x+y)(x-y) = x^2 - y^2    (that is, x squared minus y squared).

What if we let x = -4, y = Sqrt[10]?  Now can you find the product pq? 

Of course, you probably already know that given the two roots, the 
quadratic equation is

     x^2 - (p+q)x + pq = 0.

Still stumped?  Feel free to ask for details.

-Doctor Pete,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/