### Instruction: If $m$ is a real number and $x^2+mx+4$ has two distinct real roots, then what are the possible values of $m$?  Express your answer in interval notation.### Response: I know that a quadratic equation $ax^2+bx+c$ has two distinct real roots if and only if its discriminant $b^2-4ac$ is positive.
So, for this equation, I can write $b^2-4ac=m^2-16>0$ as the condition for having two distinct real roots.
I can rearrange this inequality as $m^2>16$, which means that $m$ must be either greater than 4 or less than -4.
In interval notation, I can write this as $m\in(-\infty,-4)\cup(4,\infty)$.
This is the set of all possible values of $m$ that make the equation have two distinct real roots.