Quadratic Equation - Nature of roots

(a)Find the value of m for which the line $\displaystyle y=mx-3$ is a tangent to the curve $\displaystyle y=x+\frac{1}{x}$ and find the x-coordinate of the point at which this tangent touches the curve.

(b) Find the value of c and of d for which $\displaystyle (x:-5<x<3)$ is the solution set of $\displaystyle x^2+cx<d$

For (a), how do I actually solve the quadratic equation when the equation have a $\displaystyle x^{-1}$?

No idea how to solve (b)... The whole question is just like alien to me....