SOLUTION: {{{x^2-x-1=0}}}I thought it had no real solution, but I guess I did it wrong.

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Question 19276: x%5E2-x-1=0I thought it had no real solution, but I guess I did it wrong.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The discriminant can be used to determine the nature of the solutions to the quadratic equation.
The discriminant is: b%5E2+-+4ac this is just the part under the radical of the quadratic formula: x+=+%28-b%2B-sqrt%28b%5E2+-+4ac%29%29%2F2a
If the discriminant is negative, the solutions are not real, you have two complex conjugate roots.
If the discriminant is positive, the two roots are real.
If the discriminant is zero, you have one real root (a double root)
Let's check the discriminant of your quadratic equation.
%28-1%29%5E2+-+4%281%29%28-1%29 = 1+%2B+4+=+5 The disriminant is positive, therefore, there are two real roots. What are they?
x+=+%28-%28-1%29%2B-sqrt%28%28-1%29%5E2+-+4%281%29%28-1%29%29%29%2F2%281%29
x+=+%281%2B-sqrt%285%29%29%2F2
x+=+%281%2F2%29+%2B+%281%2F2%29sqrt%285%29 and/or x+=+%281%2F2%29-%281%2F2%29sqrt%285%29