Question

If the equation x^3-3ax^2+3bx-c=0 has positive and distinct roots then
A).a^2>b
B).ab>c
C).a^3>c
D).a^3>b^2>c

Answer 1

Find the discriminant of the cubic function,
https://en.wikipedia.org/wiki/Discriminant

If D>0, the equation has 3 distinct real roots,
if D=0, the equation has multiple roots, and all roots are real.
if D<0, then equation has 1 real and 2 complex conjugate roots.

The hard part here would be to remember the general form of the discriminant of a cubic function.

Answer 2

@hartnn u said that if D>0 then roots are distinct..
But they would be distinct even for D<0

Answer 3

right, but 2 of the roots won't be real

Answer 4

so there is no question of them being positive

Answer 5

They won't be ..
And the question has not even mentioned if they r real or not..

Answer 6

they are positive means they are real.

there is no notion of positiveness in complex numbers.

Answer 7

Never thought of this !
I thought that they can be anything positive or negative..

Answer 8

if we call 1+i as positive complex no.

-1-i as negative complex number

what do we call 1-i or -1+i as ??
see the confusion/absurdness?

Answer 9

We can't figure out which is positive and which one is negative..
Ain't it??

Answer 10

yeah

so what did u get the answer for this problem?

Answer 11

Well! I have not tried that determinant..
As we have till now studied only the determinant of quadratic equation...

Answer 12

Is there any other way out to get through the motive of the problem?

Answer 13

couldn't think of other ways..

Answer 14

Do i have to solve that determinant now??

Answer 15

Don't we apply dy/dx should b greater than 0 or less than 0 conditions here??
Don't know bt thought of that randomly.?

Answer 16

For a polynomial to have n distinct zeroes it must intersect with x - axis at n points...

Answer 17

Now, you have a cubic polynomial and you want to have 3 positive and distinct roots that means that the graph should look something like this... ?