Roots

[Richard B]

What are the roots of

I don't know where to start.

 

[MarkFL]

The roots are the values of \(x\) which make the expression equal to zero. So begin by writing:

[MATH]x^2-2x+2=0[/MATH]
Have you been taught methods for solving quadratics? Like factoring, completing the square, or applying the quadratic formula?

 

[Richard B]

yes, I knew that part but I cannot come up with two numbers whose sum is -2 but product is 2

 

[HallsofIvy]

You know what part? MarkFl mentioned four different methods, factoring, completing the square, and the quadratic formula. You say you can "cannot come up with two numbers whose sum is -2 but product is 2". Are you expectng integers? There are no such integers but there are irrational numbers that will do that.

"Factoring" is only reasonable with integers but "completing the square" and the "quadratic formula" will work with all numbers.

To use "completing the square", observe that \(\displaystyle (x- 1)^2= x^2- 2x+ 1\) so we can write \(\displaystyle x^2- 2x+ 2= x^2- 2x+ 1+ 1= (x- 1)^2+ 1= 0\). Then \(\displaystyle (x- 1)^2= -1\), \(\displaystyle x- 1= pm i\), \(\displaystyle x= 1\pm i\) where i is the imaginary unit.

 

[Steven G]

As the last two posters hinted, if you have multiple methods to do a problem and one method does not work then try another method. This is logical thinking that comes from studying math. You need to start seeing that logic.

 

[Richard B]

Thank you I used the quadratic formula and I got the correct answer

 

[MarkFL]

Let's look at the discriminant...what is it?

 

[Richard B]

-2^2-4*2 or -4

 

[Steven G]

-2^2-4*2 or -4

-2^2-4*2 = -(2^2) - (4*2) = -(4)-(8) = -4-8 = -12 NOT -4

Possibly you meant (-2)^2-4*2 = -4??

 

[topsquark]

yes, I knew that part but I cannot come up with two numbers whose sum is -2 but product is 2

If you can't find such a pair of integers that means you cannot factor the problem as (x + a)(x + b) where a and b are integers. Then you have to use other methods.

-Dan

 

[Richard B]

Ok thank you