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?

Well, if those a,b,c values are indeed correct, that velocity ain't gonna be zero! — imranfat, Mar 05 '15 at 18:19
The issue here is not that $a$ and $c$ are positive, but that $4ac>b^2$. — KSmarts, Mar 05 '15 at 18:19

score 1 · Answer 1 · answered Mar 05 '15 at 18:19

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.

answered Mar 05 '15 at 18:19

ajotatxe

65,084

ok well my a = 3, b = -24 and c= 45. – Omeed Mar 05 '15 at 18:20
In this case $b^2=576$ and $4ac=540$. Then $b^2-4ac=36$, positive. – ajotatxe Mar 05 '15 at 18:22

score 0 · Answer 2 · answered Mar 05 '15 at 18:20

0

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

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

answered Mar 05 '15 at 18:20

Frank Vel

5,339

@Omeed Why don't you provide us with the question? If you only give the a,b,c values, we can't compare – imranfat Mar 05 '15 at 18:22

score 0 · Answer 3 · answered Mar 05 '15 at 18:24

0

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 $0$.

answered Mar 05 '15 at 18:24

Michael Hardy

1

I greatly suspect that's indeed what it is. Hence I asked him to provide us with the question... – imranfat Mar 05 '15 at 18:28

quadratic formula when a and c are positive?

3 Answers3