maheshmeghwal9
  • maheshmeghwal9
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.
Mathematics
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

blockcolder
  • blockcolder
So your question is...?
maheshmeghwal9
  • maheshmeghwal9
my ques is why a<0.under what coditions?
maheshmeghwal9
  • maheshmeghwal9
sorry,under what conditions?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

maheshmeghwal9
  • maheshmeghwal9
this is a question of theory of equations.
blockcolder
  • blockcolder
Do you have other assumptions on the cubic equation, like, how many solutions does it have, or other stuff like that?
maheshmeghwal9
  • maheshmeghwal9
no I don't know about the solutions but I know that this is a thoughtful question.
maheshmeghwal9
  • maheshmeghwal9
this is only verify and prove question.
anonymous
  • anonymous
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
maheshmeghwal9
  • maheshmeghwal9
but question is is true because my sir has solved it and i have lost that paper on which sir solved that.
freckles
  • freckles
I don't understand the question. You want us to solve for x? Is that what your asking?
anonymous
  • anonymous
http://www.sosmath.com/algebra/factor/fac11/fac11.html
maheshmeghwal9
  • maheshmeghwal9
what is this?
maheshmeghwal9
  • maheshmeghwal9
one more thing about this quetion
maheshmeghwal9
  • maheshmeghwal9
all the roots of this cubic equations are real
freckles
  • freckles
Oh ok now the question makes more sense. lol/
freckles
  • freckles
Omg I'm sorry. My page got killed when I was typing all of that. :(
maheshmeghwal9
  • maheshmeghwal9
np!
freckles
  • freckles
@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....
maheshmeghwal9
  • maheshmeghwal9
ok np. :(
freckles
  • freckles
i'm still thinking :(
freckles
  • freckles
@KingGeorge any thoughts?
KingGeorge
  • KingGeorge
Sorry for asking this, but just to clarify, you're asking for conditions under which a will be less than 0 correct?
freckles
  • freckles
What do you think about taking the contrapositive?
KingGeorge
  • KingGeorge
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.
KingGeorge
  • KingGeorge
If we drew the graphs, \(a\) negative would look similar to this:|dw:1336193429080:dw|And \(a\) positive would look someting like|dw:1336193456467:dw|
KingGeorge
  • KingGeorge
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.
maheshmeghwal9
  • maheshmeghwal9
thanx!
KingGeorge
  • KingGeorge
You're welcome.
freckles
  • freckles
yes thanks george :)
maheshmeghwal9
  • maheshmeghwal9
you both are good helper.
freckles
  • freckles
george is bester!
KingGeorge
  • KingGeorge
Thank you guys :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.