Question 127225
discriminate the solutions of the quadratic equation: x squared + 5x + 3 + a.
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The discriminant of a quadratic is b^2-4ac
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Your quadratic has a = 1, b=5, c=3+a
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Your discriminant is 5^2 -4*1*(3+a) = 25-12-4a = 13-4a
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When the discriminant is less than zero you have no Real Number solutions:
13-4a < 0
4a>13
a > 13/4
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When the discriminant is equal to zero you have two equal Real number solutions:
13-4a = 0
4a = 13
a = 13/4
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when the discriminant is greater than zero you have two unequal Real number 
solutions:
13-4a >0
4a<13
a < 13/4
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Cheers,
Stan H.