# imaginary numbers....

• Jun 26th 2010, 11:16 AM
Veronica1999
imaginary numbers....
Which one of the following statements is not true for the equation ix(squared) - x + 2i =0 where i = root -1?

a. the sum of the roots is 2
b. the discriminant is 9
c. the roots are imaginary
d. the roots can be found by using the quadratic formula
e. the roots can be found by factoring, using imaginary numbers

I guessed the answer is a because the sum of the roots should be -1/i.
What is i? I don't understand the problem at all.
Does i stand for imaginary numbers?
When do I use imaginary numbers?
• Jun 26th 2010, 04:19 PM
mr fantastic
Quote:

Originally Posted by Veronica1999
Which one of the following statements is not true for the equation ix(squared) - x + 2i =0 where i = root -1?

a. the sum of the roots is 2
b. the discriminant is 9
c. the roots are imaginary
d. the roots can be found by using the quadratic formula
e. the roots can be found by factoring, using imaginary numbers

I guessed the answer is a because the sum of the roots should be -1/i.
What is i? I don't understand the problem at all.
Does i stand for imaginary numbers?
When do I use imaginary numbers?

You are told in the question itself what i is. If you have never learned about imaginary numbers, I'm not sure why you are attempting a question like this.

The given equation can be re-written (by dividing both sides by i) as [tex]x^2 + ix + 2 = 0 (note that 1/i = -i ....).

If you now apply the quadratic formula to this you get x = i or x = -2i ....
• Jun 26th 2010, 06:12 PM
Veronica1999
Quote:

Originally Posted by mr fantastic
You are told in the question itself what i is. If you have never learned about imaginary numbers, I'm not sure why you are attempting a question like this.

The given equation can be re-written (by dividing both sides by i) as [tex]x^2 + ix + 2 = 0 (note that 1/i = -i ....).

If you now apply the quadratic formula to this you get x = i or x = -2i ....

Now I understand why c d and e are true.
I was just curious how a negative number could be in a square root.
At first it didn't make sense, but google helped a lot.
I am still not sure why b is true.
Can you show me?
• Jun 26th 2010, 06:28 PM
Prove It
Quote:

Originally Posted by Veronica1999
Now I understand why c d and e are true.
I was just curious how a negative number could be in a square root.
At first it didn't make sense, but google helped a lot.
I am still not sure why b is true.
Can you show me?

Looking at the original equation

\$\displaystyle i\,x^2 - x + 2i = 0\$

you have \$\displaystyle a = i, b = -1, c = 2i\$.

So \$\displaystyle \Delta = b^2 - 4ac\$

\$\displaystyle = (-1)^2 - 4(i)(2i)\$

\$\displaystyle = 1 - 8i^2\$

\$\displaystyle = 1 + 8\$

\$\displaystyle = 9\$.