Answer: The answer is [tex]\textup{The other root is }\dfrac{8}{3}~\textup{and}q=40.
Step-by-step explanation: The given quadratic equation is
[tex]3x^2+7x-q=0\\\\\Rightarrow x^2-\dfrac{7}{3}x-\dfrac{q}{3}=0.[/tex]
Also given that -5 is one of the roots, we are to find the other root and the value of 'q'.
Let the other root of the equation be 'p'. So, we have
[tex]p-5=-\dfrac{7}{3}\\\\\\\Rightarrow p=5-\dfrac{7}{3}\\\\\\\Rightarrow p=\dfrac{8}{3},[/tex]
and
[tex]p\times(-5)=-\dfrac{q}{3}\\\\\\\Rightarrow \dfrac{8}{3}\times 5=\dfrac{q}{3}\\\\\\\Rightarrow q=40.[/tex]
Thus, the other root is [tex]\dfrac{8}{3}[/tex] and the value of 'q' is 40.
