SOLUTION: I need to use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. (it is not necessary to find the roots

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Question 234186: I need to use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. (it is not necessary to find the roots; just determine the number and types of solutions)
x^2 + 6x - 7 = 0
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
I need to use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. (it is not necessary to find the roots; just determine the number and types of solutions)
x^2 + 6x - 7 = 0
------------------------
discriminant = b^2-4ac
= 6^2-4*1*-7
= 36+28
= 64
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Since the discriminant is positive, the quadratic
has 2 unequal Real Number solutions.
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Cheers,
Stan H.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Given a quadratic equation in the form:



The discriminant is found by:



And is evaluated as follows:

Two real and unequal roots. If the discriminant is a perfect square, the roots are rational, otherwise not.

One real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors.

A conjugate pair of complex roots of the form where is the imaginary number defined by

John