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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Determine whether the following equations have a solution or not? Justify your answer. 5x2 + 8x + 7 = 0       Log On


   



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

Answer by solver91311(24713) About Me  (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 n there are always n solutions.

In this case, however, there are no REAL number solutions. That is because the discriminant, i.e. the expression under the radical in x+=+%28-b+%2B-+sqrt%28red%28+b%5E2-4ac%29+%29%29%2F%282a%29+, is less than zero:

red%28b%5E2-4ac%29=64-140=-76%3C0.

Hence, the two roots of the given equation are a conjugate pair of complex numbers of the form alpha%2B-beta%28i%29, where alpha and beta are real number coefficients and i is the imaginary number defined by i%5E2=-1