Where's the roots?

• Jul 5th 2009, 07:46 AM
shawsend
Where's the roots?
Draw a single plot showing the parabola $\displaystyle f(x)=x^2-4x+5$ and where the roots are in relation to it.
• Jul 5th 2009, 07:50 AM
malaygoel
Quote:

Originally Posted by shawsend
Draw a single plot showing the parabola $\displaystyle f(x)=x^2-4x+5$ and where the roots are in relation to it.

There are no roots.
• Jul 5th 2009, 10:24 AM
masters
Quote:

Originally Posted by malaygoel
There are no roots.

There are no real roots.
• Jul 5th 2009, 11:48 AM
Soroban
Hello, shawsend!

I don't know what they mean by "a single plot."
Since the roots are complex, how are we to graph them?

Quote:

Draw a single plot showing the parabola $\displaystyle f(x)=x^2-4x+5$
and where the roots are in relation to it.

The roots are: .$\displaystyle x \:=\:2 \pm i$

Where are they? . . . Well, they are not on the $\displaystyle xy$-plane

If we had an $\displaystyle i$-axis coming out of the $\displaystyle xy$-plane,
. . the graph might look like this:

Code:

          y|             |            *             |             *          *             |*        *             |  *    *             |    *             |    :             + - - * - - - - x           /    /           /    *         /  (2,0,1)       i/

One root is on the "floor" at (2,0,1).
The other is (2,0,-1), one unit "behind" the $\displaystyle xy$-plane.

• Jul 6th 2009, 04:41 AM
shawsend
Quote:

Originally Posted by Soroban
Hello, shawsend!

I don't know what they mean by "a single plot."
Since the roots are complex, how are we to graph them?

The roots are: .$\displaystyle x \:=\:2 \pm i$

Where are they? . . . Well, they are not on the $\displaystyle xy$-plane

If we had an $\displaystyle i$-axis coming out of the $\displaystyle xy$-plane,
. . the graph might look like this:

Code:

          y|             |            *             |             *          *             |*        *             |  *    *             |    *             |    :             + - - * - - - - x           /    /           /    *         /  (2,0,1)       i/

One root is on the "floor" at (2,0,1).
The other is (2,0,-1), one unit "behind" the $\displaystyle xy$-plane.

. . . nicer please, as in a nice illustration which clearly and unambiguously depicts the parabola, the (complex) zeros, and their relationship to one another as an educational tool to help students make the connection between the real-valued function and it's complex counterpart.