Reading the Sign

You do not need to solve a quadratic to know what its solutions look like. Compute the discriminant and read its sign. Take $2{x}^{2}+3x+4 = 0$: the discriminant is ${3}^{2}-4\cdot 2\cdot 4$, which is $9-32$, or -23. Negative, so the equation has two complex solutions and no real ones.

For this question only the sign matters, not the size. -23 and -1 both mean complex solutions; 16 and 3 both mean two real ones. The size matters once you solve: a perfect square like 16 gives answers without a root sign, while 3 leaves the square root of 3 in them.

The sign also shows on the graph. The real solutions of $a{x}^{2}+bx+c = 0$ are the x values where $y = a{x}^{2}+bx+c$ crosses the x-axis. A positive discriminant means two crossings, zero means the vertex just touches the axis, and a negative one means the parabola misses the axis entirely.