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I really need help with this question.

The coefficients $a,b,c$ of the quadratic equation $ax^2+bx+c=0$ are determined by throwing 3dice and reading off the value shown on the uppermost face of each die, so that the first die gives $a$, the second $b$ and and third $c$. Find the probabilities that the roots the equations are real, complex and equal.

I was thinking about using the fundamental formula but i'm not sure how to go about doing it. Help would be greatly appreciated.

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    Couldn't you just compute the discriminant and figure out when this is non-negative? If there are only finitely many options for the coefficients, then you should be able to just count...2012-03-14
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    The value of the discriminant $b^2-4ac$ tells you which of the three cases, with regards to the roots, you are in. For instance, there are complex roots if and only if $b^2-4ac<0$. Now find the probability that the square of the second roll is less than four times the product of the first and last rolls (or just find the number of outcomes in which that happens and multiply by $(1/6^3$). I would do two of the cases and the third would be 1 minus the sum of the probabilities of the other two.2012-03-14
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    Not absolutely sure from the wording, but probably the case "real" is meant to include the case "real and equal," so the three events are not mutually exclusive. Probably "real" and "complex" are meant to be complementary, though technically the complex numbers *include* the reals, so probability of complex is $1$. However, by "complex" the person probably means "complex non-real."2012-03-14
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    @DavidMitra But the real roots also includes the equal roots. So the event are not mutually exclusive, hence we cant have 1 minus sum of the probabilities of the other two. Answer from Patrick Da Silva show that.2012-03-14
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    @Learner Sorry. Three cases: real and distinct, real and repeated, complex (and non-real).2012-03-14
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    @Learner Of course, I'm assuming, perhaps wrongly, that this is what the OP intended.2012-03-14
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    @DavidMitra Now we got both the answer(mutually exclusive and not mutually exclusive). OP can choose any one of them.2012-03-14
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    @CJS : Can I know what you meant by "the fundamental formula"?2012-03-15

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