Posted by Anonymous on Sunday, October 3, 2010 at 6:35pm.
For this equation x^(2) + x + 2
which you can't factor
but then you can use the quadratic formula
but than why is the answer no real solutions when I can use the quadratic formula?

Algebra  Reiny, Sunday, October 3, 2010 at 6:44pm
did you mean the equation
x^2 + x + 2 = 0 ?
When you solve an equation of the form
ax^2 + bx + c =0 you are really just asking,
"where does the graph of the corresponding function
y = ax^2 + bx + c cross the xaxis"?
In your case the graph, which is a parabola, lies totally above the xaxis, thus no xintercepts , and thus no real solution.
If the b^2  4ac part of the formula is zero, there will be only one solution.
If the b^2  4ac part of the formula is positive, there will be 2 different real solutions.
If the b^2  4ac part of the formula is negative, like in your case, there will be no real solution at all.
(there will be two imaginary solutions)

Algebra  Anonymous, Sunday, October 3, 2010 at 6:47pm
thank you
I forgot about having a negative for b^2  4ac was no real solutions
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