Question 72900: determine the type of solution considering only its discriminant
x^2-9=0
4x^2+16x=0
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! First Problem:
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Given 
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Comparing this form to the standard quadratic form of
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you can see that a = 1, b = 0, and c = -9
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The discriminant is given by the equation:
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Substitute into this expression the values for a, b, and c as noted above and you get:
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Do the algebra and you get:
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Since the discriminant is a positive value you know that the type of solution leads to
two real, but unequal values for x.
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[Note that this quadratic factors easily to  which by setting each
factor equal to zero tells you that the two solutions are  and  ]
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Second problem:
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Given: 
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Comparing this equation to the standard form of the quadratic equation you can determine that
a = 4, b = 16, and c = 0
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Substituting these values into the discriminant results in:
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This reduces to:
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Since the discriminant is positive, you again can say that the solutions for x are real,
and unequal.
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In fact, you might have noticed that x can be factored from the given expression for this
problem. Therefore, x = 0 is one of the two solutions.
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Hope this helps you to understand the value of the discriminant in finding characteristics
of the answers to quadratic equations that are in standard form.
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