Question

Why in the Quadroatic formula do you have it as plus or minus?

Answer 1

The root.

Answer 2

since it is a radical it can be either negative or positive.

Answer 3

That's because the solution of the equation
x^2 = a (for any non-negative a) is
x = sqrt(a) or x = -sqrt(a)

Answer 4

i get that but your having the b negative or positive depending on the equation and i guess it can through you off at times

Answer 5

simple because a quadratic equation has degree 2 which means it should have 2 solutions

for example

x^2=4
x=2 or x=-2

Answer 6

You are dealing with an original formula that had a square, so \((-4)^2\) or \(4^2\) is going to give you 16. The root of 16 is 4. But the original 4 could have been + or -.

Answer 7

As for throwing you off, well, when you take a simple one like \(x^2+x-2\) you factor it and get two solutions. The + or - also gets you two solutions. It is actually bringing you back to two solutions, not throwing you off of one solution.

Answer 8

The plus or minus sign is used just to write the quadratic formula in an easier way without to have to write the two solutions, one with the positive sign and the other with the negative sign.

Answer 9

Good question!

I think others have explained the +/- sign (because squaring a negative number gives you a positive number). You also seem to be wondering about the - b at the beginning. That is just how the formula works out. You can derive it yourself if you follow the patterns for factoring ax^2 + bx + c, but it's not the easiest thing to do.

You can also reverse that process by building an equation with roots given by the formula for the quadratic formula and you will end up simplifying to ax^2 + bx + c.

If the formula had +b rather than -b it wouldn't work out correctly.

Answer 10

\[x = \frac{ -b \pm \sqrt{b^2 - 4ac} }{ 2a }\]

Answer 11

square root can be either + or -, the number can be a negative number or postive
example the sqrt of 25 can be either 5 or -5