Need helps with cubic: x^3 - kx^2 + 3x - 54 = 0

[Math wiz ya rite 09]

Here is the question:

Determine k and solve the equation x^3 - kx^2 + 3x - 54 = 0, if one of its zeros is the triple of another.

I call the roots a, 3a, and b, so I get the equations:

3a^2b = 54
3a^2 + 4ab = 3

But what do I do now?

If someone could show me the rest of the steps of if these are wrong correct me by Tuesday.

Thanks.
Daniel

 

[pka]

You are O.K. Just finish it.
\(\displaystyle \L\begin{array}{l}
3a^2 b = 54\quad \Rightarrow \quad b = \frac{{18}}{{a^2 }} \\
3a^2 + \left( {4a} \right)\left( {\frac{{18}}{{a^2 }}} \right) = 3 \\
\end{array}\)

 

[Math wiz ya rite 09]

You are O.K. Just finish it.
\(\displaystyle \L\begin{array}{l}
3a^2 b = 54\quad \Rightarrow \quad b = \frac{{18}}{{a^2 }} \\
3a^2 + \left( {4a} \right)\left( {\frac{{18}}{{a^2 }}} \right) = 3 \\
\end{array}\)

does that mean k equals negative 3?

 

[pka]

Well, k is the sum of the roots.
What are the roots?

 

[Math wiz ya rite 09]

Well, k is the sum of the roots.
What are the roots?

I know one is -3.

i simplified the equation to 3a^2+72/a=3. is that right.

how do i get the otehr squares determined now?

thanks in advance,

~Daniel~

 

[pka]

If a=-3, then what is b?
What is 3a?

 

[Math wiz ya rite 09]

If a=-3, then what is b?
What is 3a?

is b=2 and is 3a= -9?

 

[pka]

k is the sum of the roots.
What is k?

 

[Math wiz ya rite 09]

k is the sum of the roots.
What is k?

i dont knnow, i need to solve the equation a^3-a+24=0 to do that, but i dont know how to do it. I havent delt with cubics yet.

~thanks again,
Daniel

 

[pka]

Look, the roots are: {a,3a,b}={-3,-9,2}!