Question

I'm stuck on this problem can someone tell
me if this is right so far?
(a)find the discriminant: (b)classify the root(s) as 2real (uneaqual) roots, 1 (double) root, or
2 imaginary conjungate roots: (c)find the roots
x^2-2x=-5 my answer x=1+2i,1-2i

Answer 1

discriminant is \[b^2-4ac\] in your case a = 1, b = -2 and c = 5 because first you have to write
\[x^2-2x+5=0\] to identify a, b and c. so you get
\[(-2)^2-4\times 5=4-20=-16\]
since this is negative it means you have two imaginary roots.
\[x^2-2x=-5\]
\[(x-1)^2=-5+1=-4\]
\[x-1=\pm \sqrt{-1}=\pm 2i\]
\[x=1\pm 2i\] you got it.

Answer 2

typo above. i meant \[x-1=\pm \sqrt{-4}=\pm 2i\]

Answer 3

yes thank you