Question

When dealing with quadratic equation can you make the same equation with root like you would with real zeros?

Answer 1

@mathmale ?

Answer 2

make same equation with root?

The definition of a root is basically the zero of a function/expression.

Answer 3

Do you mean with repeated or imaginary roots?

Answer 4

I did this work and then realized that the question gave me the roots and not the only real zeros and I was wondering if either it would work the same or how to get the real zeros from the information give, to then make the equation.

Answer 5

Nicole, I think the key to this problem is understanding what it's asking for. The problem statement as written is unclear.
A root is an x-value for which the quadratic equation is true: ax^2 + bx + c = 0.
A zero is the same, except it's a value for which ax^2 + bx + c turns out to be zero (0).

Answer 6

Nicole, now that I've looked at your photo2, I understand better what you want to do.

Answer 7

Okay, so how would I take what I was given to find the only real zeros? I know how to create the equation after (from my book) but I cant find where to start with just the roots..

Answer 8

Let me start with an example: suppose the roots of a quadratic equation are 2 and 3.
We obtain the quadratic equation by multiplying out the following: (x-2)(x-3).

Now if your (complex) roots are -1+4i and -1-4i, we'd obtain the desired quadratic equation by multiplying out (to be continued)

Answer 9

By the Q(X)?

Answer 10

by multiplying out (x+1+4i)(x+1-4i) and seeing the result equal to zero.
Willing to try it?

Answer 11

Yes, I'll write it down right now. Thank you for your help!!

Answer 12

So, Nicole, you were right in that you set up a product: ( )*( ), but you didn't write "x" inside each set of parentheses as you were supposed to.
I'm so glad you were able to solve this problem. See you again! Happy New Year.

Answer 13

Would you mind checking it? @mathmale
I think I got it but I get messed up with negatives so I want to makes sure I'm right.

Answer 14

Thanks for sharing the photo. It told me in a moment what happened in your calculations. You are multiplying (4i) by (-4i). Doesn't that come out to \[-16*i ^{2}?\]

Answer 15

What value does i^2 have?

Answer 16

What value does (-16)(I^2) have?

Answer 17

Oh, I see. It would be -16i^2 because you have two "i"'s which gives it a power right?

Answer 18

Yes, that's right. Now think: what does i signify?

Answer 19

Imaginary numbers

Answer 20

\[i=\sqrt{-1}.\]

Answer 21

Now square both sides of that equation to find the value of i^2.

Answer 22

I'd say "i signifies an imaginary number." Perhaps someone else can better explain this in words. In any case, i is defined by \[i=\sqrt{-1}.\]

Answer 23

How do you square both sides? I didn't know you went any further than just that.

Answer 24

Yes, that last step is quite important if you want to obtain a quadratic equation with real coefficients.

Answer 25

\[(i)^{2}=-1. Then (-16)*i ^{2}=??\]

Answer 26

So it ends up just being 16? since a negative times a negative is positive?

Answer 27

If you do that correctly, everything in your quadratic will be real. Simplify the quadratic as much as possible and then you'll be done.

Answer 28

Right on!

Answer 29

Thank you very much! Can you help me with another here or do I have to open a new post?

Answer 30

I'd prefer you do a new post. if you could do that quickly, I still have time left in which to help you.

Answer 31

Thank you! I'll open it and tag you(: