Thread: I need help finding the zeros of a function.

The function is:



I have tried to do the following:











But I know I do not have the right answer for there is not sqrt(-21)/2 as one of the answers in the back of the book. Any help would be appreciated.

let x^2 = w then x^4 = w^2

Originally Posted by thyrgle

The function is:



I have tried to do the following:











But I know I do not have the right answer for there is not sqrt(-21)/2 as one of the answers in the back of the book. Any help would be appreciated.

just after the line how did you get ??

I get it know:


Then



Thanks dwsmith!

It is true that if ab= 0, then either a= 0 or b= 0 but that is a property of 0 only!
Saying that does NOT imply that " " or that " ".

As dwsmith said, you original equation is a quadratic in . By the way, I would be inclined to write those last two roots as (1/2)i and (-1/2)i or even -i/2, i/2. -1/2i and 1/2i are too likely to be interpreted as -1/(2i) and 1/(2i) (which, it suddenly occurs to me, are exactly (1/2)i and (-1/2)i!)

Just following up on what HallsofIvy said, here is a specific counterexample:

has , as a solution. Notice that neither nor is .

Of course, there are infinitely many other solutions to this equation.