Question 72900
First Problem:
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Given {{{x^2-9=0}}}
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Comparing this form to the standard quadratic form of 
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{{{ax^2 + bx + c = 0}}}
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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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{{{b^2 - 4*a*c}}}
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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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{{{(0)^2 - 4*(1)(-9)}}}
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Do the algebra and you get:
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{{{0 + 36 = + 36}}}
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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 {{{(x-3)*(x+3) = 0}}} which by setting each
factor equal to zero tells you that the two solutions are {{{ x=+3}}} and {{{x = -3}}}]
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Second problem:
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Given: {{{4x^2+16x=0}}}
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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 {{{b^2 - 4*a*c}}} results in:
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{{{(16)^2 - 4*4*0}}}
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This reduces to:
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{{{256 - 0 = 256}}}
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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.