SOLUTION: compute value of discriminant and give the number of real solutions of this quadratic equation. 2x^2-2x+1=0

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Question 896799: compute value of discriminant and give the number of real solutions of this quadratic equation.
2x^2-2x+1=0
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


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




So lets solve 2%2Ax%5E2-2%2Ax%2B1=0 ( notice a=2, b=-2, and c=1)





x+=+%28--2+%2B-+sqrt%28+%28-2%29%5E2-4%2A2%2A1+%29%29%2F%282%2A2%29 Plug in a=2, b=-2, and c=1




x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A2%2A1+%29%29%2F%282%2A2%29 Negate -2 to get 2




x+=+%282+%2B-+sqrt%28+4-4%2A2%2A1+%29%29%2F%282%2A2%29 Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because %28-2%29%5E2=-2%2A-2=4.)




x+=+%282+%2B-+sqrt%28+4%2B-8+%29%29%2F%282%2A2%29 Multiply -4%2A1%2A2 to get -8




x+=+%282+%2B-+sqrt%28+-4+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)




x+=+%282+%2B-+2%2Ai%29%2F%282%2A2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%282+%2B-+2%2Ai%29%2F%284%29 Multiply 2 and 2 to get 4




After simplifying, the quadratic has roots of


x=1%2F2%2B1%2F2%2Ai or x=1%2F2-1%2F2%2Ai



The discriminant is -4 and so there are no real solutions