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maheshmeghwal9
Group Title
If x^3+ax+b=0, & a,b belongs to real numbers, b is not equal to zero.Then, why a<0,since it is the a statement which holds true.And all the roots of this equation are real.
 2 years ago
 2 years ago
maheshmeghwal9 Group Title
If x^3+ax+b=0, & a,b belongs to real numbers, b is not equal to zero.Then, why a<0,since it is the a statement which holds true.And all the roots of this equation are real.
 2 years ago
 2 years ago

This Question is Closed

blockcolder Group TitleBest ResponseYou've already chosen the best response.0
So your question is...?
 2 years ago

maheshmeghwal9 Group TitleBest ResponseYou've already chosen the best response.0
my ques is why a<0.under what coditions?
 2 years ago

maheshmeghwal9 Group TitleBest ResponseYou've already chosen the best response.0
sorry,under what conditions?
 2 years ago

maheshmeghwal9 Group TitleBest ResponseYou've already chosen the best response.0
this is a question of theory of equations.
 2 years ago

blockcolder Group TitleBest ResponseYou've already chosen the best response.0
Do you have other assumptions on the cubic equation, like, how many solutions does it have, or other stuff like that?
 2 years ago

maheshmeghwal9 Group TitleBest ResponseYou've already chosen the best response.0
no I don't know about the solutions but I know that this is a thoughtful question.
 2 years ago

maheshmeghwal9 Group TitleBest ResponseYou've already chosen the best response.0
this is only verify and prove question.
 2 years ago

veramath Group TitleBest ResponseYou've already chosen the best response.0
The statement is not complete. For example: we say the standard form of quadratic equation is \[ax^2+bx+c=0, where a, b, c \in R \] and a, b not both zero
 2 years ago

maheshmeghwal9 Group TitleBest ResponseYou've already chosen the best response.0
but question is is true because my sir has solved it and i have lost that paper on which sir solved that.
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.1
I don't understand the question. You want us to solve for x? Is that what your asking?
 2 years ago

cinar Group TitleBest ResponseYou've already chosen the best response.0
http://www.sosmath.com/algebra/factor/fac11/fac11.html
 2 years ago

maheshmeghwal9 Group TitleBest ResponseYou've already chosen the best response.0
what is this?
 2 years ago

maheshmeghwal9 Group TitleBest ResponseYou've already chosen the best response.0
one more thing about this quetion
 2 years ago

maheshmeghwal9 Group TitleBest ResponseYou've already chosen the best response.0
all the roots of this cubic equations are real
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.1
Oh ok now the question makes more sense. lol/
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.1
Omg I'm sorry. My page got killed when I was typing all of that. :(
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.1
@foolformath what do you think of this problem? For some reason I was thinking about finding f' And I found critical numbers pm sqrt(a/3) I found it is increasing on (inf,sqrt(a/3)) and (sqrt(a/3),inf) and decreasing on (sqrt(a/3),sqrt(a/3)) I can't decide what to do from this or if i can do anything with what i found....
 2 years ago

maheshmeghwal9 Group TitleBest ResponseYou've already chosen the best response.0
ok np. :(
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.1
i'm still thinking :(
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.1
@KingGeorge any thoughts?
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.2
Sorry for asking this, but just to clarify, you're asking for conditions under which a will be less than 0 correct?
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.1
What do you think about taking the contrapositive?
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.2
If that's the question, looking at the derivative is a good idea. \[f(x)=x^3+ax+b\]\[f'(x)=3x^2+a\]If \(a\) is negative, then we would have 2 critical points that translate to local maxima and local minima. If a is positive, we would have 0 critical points.
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.2
If we drew the graphs, \(a\) negative would look similar to this:dw:1336193429080:dwAnd \(a\) positive would look someting likedw:1336193456467:dw
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.2
This means that if \(a\) were positive, then the function would always be increasing. Hence, we would only have one real root. But we're required to have all real roots. Contradiction! Therefore, a must be less than 0.
 2 years ago

maheshmeghwal9 Group TitleBest ResponseYou've already chosen the best response.0
thanx!
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.2
You're welcome.
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.1
yes thanks george :)
 2 years ago

maheshmeghwal9 Group TitleBest ResponseYou've already chosen the best response.0
you both are good helper.
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.1
george is bester!
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.2
Thank you guys :)
 2 years ago
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