Probability of real roots(short way)

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Each coefficient in the equation $ax^2+bx+c$ is determined by throwing an ordinary dice. Find the probability that the given equation will have real roots?
I counted the cases which fulfill D(discriminant) greater than zero, but that turned into a long method.



Is there an elegant short way to do this question?




probability




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  • How is each coefficient determined according to the die result? Also, is the die an ordinary, six sided one with numbers from $1$ to $6$ or is it arbitrarily sized? Are the coefficients $a,b,c$ real?
    – Guido A.
    Aug 3 at 7:21










  • Welcome to MSE. Please read this text about how to ask a good question.
    – José Carlos Santos
    Aug 3 at 7:25










  • Yes the die is an ordinary six sided one and as the numbers on the dice are from 1to 6 do a,b,c must be real
    – user90596
    Aug 3 at 7:27










  • It seems you need to consider cases $b leq 2 sqrtac$ and $b geq 2 sqrtac$.
    – Alex
    Aug 3 at 7:28










  • If discriminant$ b^2-4ac > 0 $then both the condition s you gave are satisfied.
    – user90596
    Aug 3 at 7:30














up vote
1
down vote

favorite
1












Each coefficient in the equation $ax^2+bx+c$ is determined by throwing an ordinary dice. Find the probability that the given equation will have real roots?
I counted the cases which fulfill D(discriminant) greater than zero, but that turned into a long method.



Is there an elegant short way to do this question?




probability




share|cite|improve this question



















  • How is each coefficient determined according to the die result? Also, is the die an ordinary, six sided one with numbers from $1$ to $6$ or is it arbitrarily sized? Are the coefficients $a,b,c$ real?
    – Guido A.
    Aug 3 at 7:21










  • Welcome to MSE. Please read this text about how to ask a good question.
    – José Carlos Santos
    Aug 3 at 7:25










  • Yes the die is an ordinary six sided one and as the numbers on the dice are from 1to 6 do a,b,c must be real
    – user90596
    Aug 3 at 7:27










  • It seems you need to consider cases $b leq 2 sqrtac$ and $b geq 2 sqrtac$.
    – Alex
    Aug 3 at 7:28










  • If discriminant$ b^2-4ac > 0 $then both the condition s you gave are satisfied.
    – user90596
    Aug 3 at 7:30












up vote
1
down vote

favorite
1









up vote
1
down vote

favorite
1






1





Each coefficient in the equation $ax^2+bx+c$ is determined by throwing an ordinary dice. Find the probability that the given equation will have real roots?
I counted the cases which fulfill D(discriminant) greater than zero, but that turned into a long method.



Is there an elegant short way to do this question?




probability




share|cite|improve this question











Each coefficient in the equation $ax^2+bx+c$ is determined by throwing an ordinary dice. Find the probability that the given equation will have real roots?
I counted the cases which fulfill D(discriminant) greater than zero, but that turned into a long method.



Is there an elegant short way to do this question?





probability





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Aug 3 at 7:18









user90596

163




163











  • How is each coefficient determined according to the die result? Also, is the die an ordinary, six sided one with numbers from $1$ to $6$ or is it arbitrarily sized? Are the coefficients $a,b,c$ real?
    – Guido A.
    Aug 3 at 7:21










  • Welcome to MSE. Please read this text about how to ask a good question.
    – José Carlos Santos
    Aug 3 at 7:25










  • Yes the die is an ordinary six sided one and as the numbers on the dice are from 1to 6 do a,b,c must be real
    – user90596
    Aug 3 at 7:27










  • It seems you need to consider cases $b leq 2 sqrtac$ and $b geq 2 sqrtac$.
    – Alex
    Aug 3 at 7:28










  • If discriminant$ b^2-4ac > 0 $then both the condition s you gave are satisfied.
    – user90596
    Aug 3 at 7:30
















  • How is each coefficient determined according to the die result? Also, is the die an ordinary, six sided one with numbers from $1$ to $6$ or is it arbitrarily sized? Are the coefficients $a,b,c$ real?
    – Guido A.
    Aug 3 at 7:21










  • Welcome to MSE. Please read this text about how to ask a good question.
    – José Carlos Santos
    Aug 3 at 7:25










  • Yes the die is an ordinary six sided one and as the numbers on the dice are from 1to 6 do a,b,c must be real
    – user90596
    Aug 3 at 7:27










  • It seems you need to consider cases $b leq 2 sqrtac$ and $b geq 2 sqrtac$.
    – Alex
    Aug 3 at 7:28










  • If discriminant$ b^2-4ac > 0 $then both the condition s you gave are satisfied.
    – user90596
    Aug 3 at 7:30















How is each coefficient determined according to the die result? Also, is the die an ordinary, six sided one with numbers from $1$ to $6$ or is it arbitrarily sized? Are the coefficients $a,b,c$ real?
– Guido A.
Aug 3 at 7:21




How is each coefficient determined according to the die result? Also, is the die an ordinary, six sided one with numbers from $1$ to $6$ or is it arbitrarily sized? Are the coefficients $a,b,c$ real?
– Guido A.
Aug 3 at 7:21












Welcome to MSE. Please read this text about how to ask a good question.
– José Carlos Santos
Aug 3 at 7:25




Welcome to MSE. Please read this text about how to ask a good question.
– José Carlos Santos
Aug 3 at 7:25












Yes the die is an ordinary six sided one and as the numbers on the dice are from 1to 6 do a,b,c must be real
– user90596
Aug 3 at 7:27




Yes the die is an ordinary six sided one and as the numbers on the dice are from 1to 6 do a,b,c must be real
– user90596
Aug 3 at 7:27












It seems you need to consider cases $b leq 2 sqrtac$ and $b geq 2 sqrtac$.
– Alex
Aug 3 at 7:28




It seems you need to consider cases $b leq 2 sqrtac$ and $b geq 2 sqrtac$.
– Alex
Aug 3 at 7:28












If discriminant$ b^2-4ac > 0 $then both the condition s you gave are satisfied.
– user90596
Aug 3 at 7:30




If discriminant$ b^2-4ac > 0 $then both the condition s you gave are satisfied.
– user90596
Aug 3 at 7:30















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