Equations Value of M one given Root

Question

The question I have is 2x^2+mx-21=0.

The area I am stuck on is finding one of the roots, one root was given as -7, however I need to find the other one.

Answer 1

Some advice

You know that $x=-7$ is a root. Thus

$f(-7)=2\cdot (-7)^2-m\cdot 7-21=0$

Solve for $m$. After you have evaluated the value ($m^*$), you conduct the polynomial division with the known root.

$(2x^2+m^*x-21):(x+7)=\ldots$

And finally you set the result of the polynomial division equal to $0$ and solve for $x$ to get the second root.