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How to solve this probability question?f a, b, and c are in the range [0, 1], what is the probability that the quadratic equation ax^2 + bx + c has real solutions? justify your answer!

This question was posed by the esteemed Portuguese mathematics educator, José Paulo Viana, during a session of the APM - Mathematics Teachers Association of Portugal(https://www.facebook.com/photo/?fbid=718336196985035&set=a.415008250651166&__cft__[0]=AZWSIZa5VPhQfEw1WoyJo9yDPREx3Y5eBshgw9sHI9RYRnobpRh_nvBUEKPwW_U4pt2Z66dX39xJa7ZJIzRoYEIYugSvksorwI-1qIymHA5CeMGqmJR-zlYWC1cxpIXQk4VExGzEeSb8ZFFUAvAn11Do91iyHUYNi9kGLiQiFBEIw0zootIC61uUahWmo8TX6OQ&__tn__=%2CO*F). It serves as an exemplary case of an engaging problem in the field of probability and has indeed captured my attention.

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    $\begingroup$ ... and why exactly would we make your homework? :-) $\endgroup$
    – Dominique
    Nov 9, 2023 at 15:56
  • $\begingroup$ Hint: It is a volume computation involving the discriminant. $\endgroup$
    – Adam
    Nov 9, 2023 at 18:23
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    $\begingroup$ Please edit so that the connection with math education is clear. Otherwise, we will need to close this question. $\endgroup$
    – Sue VanHattum
    Nov 9, 2023 at 19:37
  • $\begingroup$ @SueVanHattum, done! $\endgroup$ Nov 10, 2023 at 22:00
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    $\begingroup$ 5 users voted for it to be closed. I suggest asking in mathse $\endgroup$
    – Sue VanHattum
    Nov 10, 2023 at 23:07

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This sounds like a homework question, but it seems you're a professor with publications and years of history on the site, so I'll give you the benefit of the doubt and assume you're asking for a good reason (though it would probably be worth editing your post to explain what that reason is).

This question has been asked before on Math.SE (here and here) where it has received plenty of thorough answers, all arriving at the same result. (If there are specific questions you have about those solutions, it would also be worth editing your post to explain what your specific questions are.)

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    $\begingroup$ This should have been a comment, not an answer. $\endgroup$
    – JRN
    Nov 10, 2023 at 5:52
  • $\begingroup$ @justin, Math. Se accepts only research question in Mathematics not basic school ones likr this. nevertheless you links were very useful. Thanks. $\endgroup$ Nov 11, 2023 at 12:46

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