SOLUTION: Determine whether the following equations have a solution or not? Justify your answer. 5x2 + 8x + 7 = 0

Question 144718: Determine whether the following equations have a solution or not? Justify your answer.
5x2 + 8x + 7 = 0

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Of course there is a solution, in fact there are two solutions -- there always are when you have a quadratic equation. The fundamental theorem of algebra tells us that for a polynomial equation of degree there are always solutions.

In this case, however, there are no REAL number solutions. That is because the discriminant, i.e. the expression under the radical in , is less than zero:

.

Hence, the two roots of the given equation are a conjugate pair of complex numbers of the form , where and are real number coefficients and is the imaginary number defined by
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