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 }(8)/(3)~\textup{and}q=40.</strong></p><p></p><p><strong>Step-by-step explanation:  </strong>The given quadratic equation is</p><p>[tex]3x^2+7x-q=0\\\\\Rightarrow x^2-(7)/(3)x-(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=-(7)/(3)\\\\\\\Rightarrow p=5-(7)/(3)\\\\\\\Rightarrow p=(8)/(3),`

and

`p*(-5)=-(q)/(3)\\\\\\\Rightarrow (8)/(3)* 5=(q)/(3)\\\\\\\Rightarrow q=40.`

Thus, the other root is
`(8)/(3)` and the value of 'q' is 40.