Question

Find the zeros of (x^2+4) (x-3)

Answer 1

A multiplication is zero if and only if at least one of the factors is zero. So, in this case, the multipications equals zero when

$x^2+4 = 0 \quad \lor \quad x-3=0$

The first equation has no real solutions, because $x^2$ is a square, and thus it's positive. If you add 4 to a positive number, the result can't be zero.

The second equation has the solution

$x-3=0 \iff x=3$

So, globally, the expression equals zero if and only if $x=3$