Quadratic Formula: When to Use it?

[Lukeitfc]

I know this is a basic question, but can someone please help me with WHEN to use the quadratic formula, i just wondered, can it be used on any quadratic?

 

[The Bob]

I know this is a basic question, but can someone please help me with WHEN to use the quadratic formula, i just wondered, can it be used on any quadratic?

If a quadratic equation can be factorised then that is easier but you normally only use it when you can't factorise the quadratic and you want to know what x is.

The Bob (2004 ©)

 

[Lukeitfc]

thanks mate, just wonderin

 

[James R]

You can use it whenever you want to solve for the roots (solutions) of an equation of the form:

$$ax^2 + bx + c = 0$$

It works for any equation of this form. However, in some cases, it is unnecessary, as The Bob has already said. For example, if you have

$$2x^2 + 4x - 6 = 0$$

this factorises to give

$$2(x - 1)(x + 3) = 0$$,

and you can see immediately that the solutions are x=1 or -3.

 

[Diane_]

It's worth noting, I think, that the quadratic formula works on anything that can be expressed in quadratic form. For instance, if you have an equation like

sin^2(x) + 2sin(x) - 2 = 0

you can use the quadratic formula to solve for sin(x) - the equation is quadratic in sin(x).

If you have an equation like

x^4 - 3x^2 + 5 = 0

you can use the quadratic formula to solve for x^2: the equation is quadratic in x^2. This last may be seen more easily if we use the substitution y = x^2: in that case, we have

y^2 -3y + 5 = 0

This is obviously a case where the quadratic formula applies. You use it to solve for y, then remember that y = x^2.

There are a lot of places where this knowledge comes in very handy.

 

[Sirus]

If a quadratic equation can be factorised then that is easier but you normally only use it when you can't factorise the quadratic and you want to know what x is.

The correct term is factor, not factorise.

 

[Diane_]

The correct term is factor, not factorise.

You're speaking American. He's speaking English. :)

 

[Sirus]

Hmm, after some brief googling action, I think you're right. However, my claim was not baseless: I checked my Merriam-Webster's Dictionary, and factorise is not listed as a word, while factor is; one of the definitions is, of course, the mathematical one with which we are concerned here. It is an American dictionary, though, so I guess that explains it.

 

[Raza]

for someone who knows history, how did the Neolithic use the quadratic equation?
The Neolithic Age was before the first civilization.

 

[Diane_]

for someone who knows history, how did the Neolithic use the quadratic equation?
The Neolithic Age was before the first civilization.

If you mean the quadratic formula, they didn't. The Neolithic (New Stone) Age was before the development of formal mathematics.

If you mean quadratics in general - again, they didn't. Same reason.

If you mean situations inwhich quadratics are used today to describe them, then there were a lot. Quadratics, for instance, do a good job of describing the path a rock or a spear takes when thrown (if air resistance is neglected). I doubt, however, that someone without a written language would be capable of, or for that matter need to, solve something like that to catch dinner.