Sunday, May 14, 2006
19:05
On Friday, when I walked into the room before the first class with the homeschoolers, the teacher handed me a paper with a problem on it. It was the extra credit problem from the test that the algebra class (second hour) had just done, and he hadn't had time to find the solution for when they asked about it. Here's the problem:
The roots of a quadratic equation are 1 + sqrt(5) and 1 - sqrt(5). Find the equation.
There's a more difficult way to do it that finds an infinite family of solutions, and an easier way that finds just one solution. I demonstrated the more difficult way to the class, because that's what I thought of, but then a few minutes afterwards the easier method occurred to me so I showed them that as well.
The roots of a quadratic equation are 1 + sqrt(5) and 1 - sqrt(5). Find the equation.
There's a more difficult way to do it that finds an infinite family of solutions, and an easier way that finds just one solution. I demonstrated the more difficult way to the class, because that's what I thought of, but then a few minutes afterwards the easier method occurred to me so I showed them that as well.
# posted by Fibonacci @ 14.5.06 
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Hi...Was good talking to you. Sorry I had to go eat before we had time to end our talk. You too needed to eat I guess. Uncle Randy called when I got home tonight. Alls okay with him.
As for your class room solutions,it is greek to G_Ma you know. Didn't know you could teach Greek huh??? Love Ya
As for your class room solutions,it is greek to G_Ma you know. Didn't know you could teach Greek huh??? Love Ya
# posted by 
: 9:34 PM
: 9:34 PM
*considers* x^2-2x-4? I'm surprised you didn't see the very simple way of (x-r1)(x-r2), where r1 and r2 are the desired roots, first. Then you can multiply by any constant for the more generic version.
In Math143, there would usually be an extra condition to make it unique. "leading coefficient 1" or "f(5)=2"
*shrugs*
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In Math143, there would usually be an extra condition to make it unique. "leading coefficient 1" or "f(5)=2"
*shrugs*
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