quadratic formula when a and c are positive?

Question

How can you do the quadratic forumla when a and c are positive? I am in a calc class trying to find when the velocity is 0 with a given quadratic equation. But when a and c are positive you get a negative square root, no?

ex)

$$a= 4,\quad b= 3,\quad c= 5$$

$$b^2-4(4)(5)$$

$4 \cdot 4 \cdot 5$ will be positive.

$3$ minus a positive $=$ a negative.

but you can't do a square root of a negative?

Answer 1

If $a$ and $c$ are both positive, then $b^2-4ac$ can be positive or negative.

If $4ac<b^2$ then $b^2-4ac$ is positive and, as you surely know, the equation has two roots.

Answer 2

A counterexample: $a=1,\,b = 5,\,c=2$

$b^2-4ac = 5^2-4\times1\times4 = 25-16 = 9 > 0$

Answer 3

Might it be that location is given by a quadratic polynomial and velocity by its derivative? In that case, it's the derivative, not the original quadratic polynomial, that you would set equal to $0$.