SOLUTION: Could someone please help me with this proble? Determine the number of solutions and classify the type of solutions for the following equation and justify the answer. x^2 +

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Question 204107: Could someone please help me with this proble?
Determine the number of solutions and classify the type of solutions for the following equation and justify the answer.

x^2 + 3x - 15 = 0
my answer is that there are two solutions x = 2.65, -5.65 but I'm not sure how to classify the type of solution and justify it.
Found 2 solutions by RAY100, solver91311:
Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website!
Your answers are correct,,,,very good.
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They want us to recognize the value of the DISCRIMINANT ,,(b^2 -4ac)
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with a=1,,,,b=3,,and, c= -15),,,,D={(3)^2- 4(1)(-15)}={9+60}=69
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The discriminant rules are:
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D=0,,,one solution, curve intersects x axis at one location
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D>0,,,,two solutions,,,as in this case,curve intersects x axis in 2 locations
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D<0,,,,no Real solutions,,,,,,,,curve does not intersect x axis

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

The Fundamental Theorem of Algebra says that any polynomial equation of the form:

Has roots. So your equation must have two roots.

The Discriminant, , is the portion of the quadratic equation under the radical in the quadratic equation, namely:

, where the given equation is

Classify the roots as follows.

Two real and unequal roots. If is not a perfect square, then the two roots are a conjugate pair of irrational numbers of the form where and

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

By the way, your claim that the roots are and is not precisely correct. If you want to express the roots as decimals, the best you can do is express them as an approximation. So you should have said and . The only way to express the roots exactly is to leave the answers in radical form, namely

John