My techer asked me to submit the answer for this question by tomorrow.
I cracked my brain for 2hrs but it did'nt help me.
Question: If the 2 roots of ax<sup>3</sup>+bx<sup>2</sup>+cx+d=0 are equal, find the relation between a,b,c,d?

My techer asked me to submit the answer for this question by tomorrow.
I cracked my brain for 2hrs but it did'nt help me.
Question: If the 2 roots of ax<sup>3</sup>+bx<sup>2</sup>+cx+d=0 are equal, find the relation between a,b,c,d?
consider the roots x,y,z. x=y. then use the formula. x+y+z=b/a and xy+yz+zx=c/a and xyz=d/a. simplify and u will get the answer
thats a third grade equation, it can be up to 3 answers
Well ashwini9688's solution may be correct but perhaps this is more helpful. Multiply out the followng:Originally Posted by anandsatya
(x  u)(x  u)(v x  w)
then equate the coefficients of the x^3 term with a and of the x^2 term with b and of the x term with c and the constant term with d. That will give what we call a parametric relationship between a, b, c and d. You can eliminate the u, v and w to get the direct relationships between a, b, c and d. But since this involves the algebraic solution of a cubic equation I don't know if this last step is worth the trouble, I would just stick with the parametric relations, or a least eliminate only v and w, but not v.
Unsolvable in my opinion. you need to know more. There are three possible roots, and even if you knew all three, they could all equal any constant, and you probably wouldnt even be able to find a, b, c, and d then.
your's question will be difficult i cant answer this
if u know the answer plese mail the answer to my persional mail
mail id is: reddaiah224@gmail.com
I think you made a mistake (or a typo) there: I think you mean if the 3 roots of the equation are equal. If only two are equal, it's unsolvable  even if you handpick a value for the repeated root, you still won't be able to solve it.Originally Posted by anandsatya
Say, suppose the repeated root is 0 and the other root is k. Then you have c = d = 0 and k = b/a, and that's all you can do. You still can't get any relation between a and b in this particular case.
However, if all three roots are equal, then you can indeed get a relation between the coefficients. You have
and you can eliminate k to get 9ad = bc.
Suppose the roots of the cubic equation are all real and positive.
Prove that .
8)
I'm not sure the inequality is correct.Originally Posted by JaneBennet
I've seen something like that before, you use the fact that the arithmetic mean of a set of positive integers is never less than their geometric mean.
Let the three positive roots be . So
Also
However you can only conclude that and are both greater than or equal to , you can't conclude that .
For you need to use the Cauchy–Schwarz inequality.
Cauchy–Schwarz says that
Now use to complete the job. 8)
you can start with 0 =< (ab)^2+(bc)^2+(ca)^2 = 2(a^2+b^2+c^2)2(ab+bc+ca)Originally Posted by JaneBennet
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