SOLUTION: If α and β are the roots of 2x²-2x+5=0, find the values of (1/α+1)+(1/β). Hence determine the nature of the roots.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: If α and β are the roots of 2x²-2x+5=0, find the values of (1/α+1)+(1/β). Hence determine the nature of the roots.       Log On


   

Question 1132053: If α and β are the roots of 2x²-2x+5=0, find the values of (1/α+1)+(1/β).
Hence determine the nature of the roots.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2-2x%2B5=0+
we need to use quadratic formula to find roots
and, to determine the nature of the roots we can check if discriminant is <+0,
if b%5E2+-+4ac+%3C+0+ then, as we know, the roots are+imaginary+values
%28-2%29%5E2+-+4%2A2%2A5+%3C+0+
4+-+40+%3C+0+
-+36+%3C+0+=> the roots are imaginary

now use quadratic formula to find roots

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A2%2A5+%29%29%2F%282%2A2%29+
x+=+%282+%2B-+sqrt%28+4-36%29%29%2F4+
x+=+%282+%2B-+sqrt%28+-32%29%29%2F4+
x+=+%282+%2B-+sqrt%28+-2%2A16%29%29%2F4+
x+=+%282+%2B-+4sqrt%282%29%2Ai%29%2F4+...simplify

x+=+%281+%2B-+2sqrt%282%29%2Ai%29%2F2+

roots:
x+=+%281+%2B2sqrt%282%29%2Ai%29%2F2+
x+=+%281+-+2sqrt%282%29%2Ai%29%2F2+

let alpha=+%281+%2B2sqrt%282%29%2Ai%29%2F2+ and beta=%281+-+2sqrt%282%29%2Ai%29%2F2+
then,






Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
My internal feeling says me that the post is incorrect.

Double check your input with your source.