<s>[INST] Product and Sum of Polynomial Roots The ratio of the sum of the roots of the equation, $8x^3+px^2-2x+1=0 $  to the product of the roots of the equation $5x^3+7x^3-3x+q=0 $ is $3:2$. What is the value $\frac{p-q}{p+q}$?
Well I found out the sum of the roots of 1st equation is $-\frac{p}{8}$ and product of roots of second equation is $-\frac{d}{5}$.
Now what to do further? How to get in terms of $\frac{p-q}{p+q} $ ?
 [/INST] Using Vieta's Formulas,
the sum of the roots of  $\ 8x^3+px^2-2x+1=0$ is $\frac{-p}8$  
and the product of the roots of $\ 5x^3+7x^3-3x+q=0$ is $\frac {-q}5$
So, $$\frac {\frac{-p}8}{\frac {-q}5}=\frac32\implies \frac pq=\frac{3\cdot 8}{2\cdot 5}=\frac{12}5$$
Now, use Componendo and dividendo
or use $$\frac{p-q}{p+q}=\frac{\frac pq-1}{\frac pq+1}=\frac{\frac {12}5-1}{\frac {12}5+1}=\frac{12-5}{12+5}$$
or use  $$\frac p{12}=\frac q5=r(\ne0)\text{(say)}\implies p=12r,q=5r$$
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