Question 1099436
.
<pre>
According to Vieta's theorem, the product of the roots is equal to the constant term taken with the opposite sign in this case.


In the mathematical form,  p*(2p)*(3p) = 48,   or

6p^3 = 48  ====>  p^3 = {{{48/6}}} = 8  ====>  p = {{{root(3,8)}}} = 2.


<U>Answer</U>.  p = 2.
</pre>


It is INTERESTING that under the given condition, the answer <U>DOES NO DEPEND</U> on the value of the coefficient "a" of the given equation.



<pre>
    In opposite, by knowing all the roots p= 2, 2p = 4  and  3p= 6, we can calculate the coefficient "a" 

    (using again the Vieta's theorem) as the sum of all pair-wise products of the roots:


    a = 2*4 + 2*6 + 4*6 = 8 + 12 + 24 = 44.
</pre>