Finding Roots

March 19, 2010
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Crystal Fantry
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Steven Strogatz, a professor of applied mathematics at Cornell University, is currently blogging for The New York Times about issues “from the basics of math to the baffling”. It’s been a fascinating series, starting with preschool math and progressing through subtraction, division, complex numbers, and more. As Wolfram|Alpha is such a powerful tool for working with mathematical concepts, we thought it’d be fun to show how to use it to explore some of the topics in Strogatz’s blog.

First up is Strogatz’s post on “Finding Your Roots”. For a brief introduction to Wolfram|Alpha’s ability to find roots, try “root of 4x+2”.
Wolfram|Alpha solves "root of 4x+2"

Here we found the one and only root of 4x+2, but what if there is more than one root? Not a problem for Wolfram|Alpha—try “4x^2 + 3x – 4”.

Wolfram|Alpha finds the roots of 4x^2+3x-4 for x

Of course, Wolfram|Alpha has the ability to find complex roots as well. Try “solve x^2-10x+34 for x”.

Wolfram|Alpha solves x^2 - 10x + 34 for x

Here you can see the complex roots of the quadratic function and a visual representation of the roots, as well as the steps to the solution.

You can even try to stump Wolfram|Alpha with a trig function, such as “roots of e^x*(x^3+4x-2)”.

Wolfram|Alpha solves "roots of e^x*(x^3+4x-2)"

If you want to make this a little more complicated, enter  “solve e^(x – 3) = -x + 2” into Wolfram|Alpha.

Wolfram|Alpha solves e^(x-3) = -x +2

Now that you have seen a few examples of what Wolfram|Alpha can do, try your hardest problem.

5 Comments

Plz, what is the solution of this equation:
x^(5/3)-1=0;

Posted by Tag Mohamed Amine March 19, 2010 at 6:22 pm Reply

Sorry I need the solution of this equation:
x^(5/3)+1=0

Posted by Tag Mohamed Amine March 19, 2010 at 6:24 pm Reply

I had a fun time playing around with this tool. A friend of mine studies informatics and I bet he’s going to love it!

Posted by warrior guide July 15, 2010 at 2:32 am Reply

This is a great setup, I was never this deep into math but my daughter is. I like the layout, great webmaster…

Posted by Live Prayer February 10, 2012 at 2:08 am Reply

Great examples! Would it be possible to add an example of finding a root of a trigonometric function?

Posted by Drake Cennedig October 11, 2012 at 12:52 am Reply
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