Question

One of the roots of the equation 3x^2+7x−q=0 is −5. Find the other root and q.

Answer 1

Answer: The answer is $\textup{The other root is }\dfrac{8}{3}~\textup{and}q=40.Step-by-step explanation: The given quadratic equation is[tex]3x^2+7x-q=0\\\\\Rightarrow x^2-\dfrac{7}{3}x-\dfrac{q}{3}=0.$

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

$p-5=-\dfrac{7}{3}\\\\\\\Rightarrow p=5-\dfrac{7}{3}\\\\\\\Rightarrow p=\dfrac{8}{3},$

and

$p\times(-5)=-\dfrac{q}{3}\\\\\\\Rightarrow \dfrac{8}{3}\times 5=\dfrac{q}{3}\\\\\\\Rightarrow q=40.$

Thus, the other root is $\dfrac{8}{3}$ and the value of 'q' is 40.