# How to do quadratic formula?

• Jun 25th 2013, 08:37 PM
minneola24
I have an equation 2x^2+x-1

How do I rewrite in parenthesis? Like (x+ )(x- )
Etc.

I got x = .5 and -1 using quadratic formula
Thanks
• Jun 25th 2013, 08:51 PM
ReneG
Re: How to do quadratic formula?
Just a heads up, this isn't a calculus problem.

Anyways, I believe you can only factor a quadratic $\displaystyle ax^2 +bx+c$ strictly into the form $\displaystyle (x + h)(x+k)$ when $\displaystyle a=1$

You can still factor by grouping though.
• Jun 25th 2013, 09:06 PM
Prove It
Re: How to do quadratic formula?
Quote:

Originally Posted by minneola24
I have an equation 2x^2+x-1

How do I rewrite in parenthesis? Like (x+ )(x- )
Etc.

I got x = .5 and -1 using quadratic formula
Thanks

To start with, you need to find two numbers that multiply to give "ac" and add to give "b".
• Jun 26th 2013, 02:47 AM
ibdutt
Re: How to do quadratic formula?
In general for a quadratic equation ax^2 + bx + c = 0 for factorization just write the product of the coefficient of x^2 and constant, in this case ac. Thereafter find such factors of the product ac such that their sum is equal to the coefficient of x. there after split the middle term and group into factors.
• Jun 26th 2013, 06:10 AM
minneola24
Re: How to do quadratic formula?
The reason I put it in calculus is because im doing a partial fraction integral and need to seperate the denomenamtor.

I'm still confused how to use the quadratic formula to factor into (x )(x )

Because I get .5 and -1 from the quadratic formula

However graphing (x-.5)(x+1) does not give the same as the original equation :S
• Jun 26th 2013, 06:48 AM
Plato
Re: How to do quadratic formula?
Quote:

Originally Posted by minneola24
I have an equation 2x^2+x-1
How do I rewrite in parenthesis? Like (x+ )(x- )
Etc.
I got x = .5 and -1 using quadratic formula

.

It is simple: $\displaystyle ax^2+bx+c$ can always be factored,
$\displaystyle \left( {x - \frac{{ - b + \sqrt {{b^2} - 4ac} }}{{2a}}} \right)\left( {x - \frac{{ - b - \sqrt {{b^2} - 4ac} }}{{2a}}} \right)$.
• Jun 26th 2013, 06:55 AM
HallsofIvy
Re: How to do quadratic formula?
Perhaps it is that "2" that is bothering you knowing that .5 and -1 are roots of the polynomial tells you that you want $\displaystyle (x- .5)(x- (-1))= (x- .5)(x+ 1)$ However, with that "2" coefficient of $\displaystyle x^2$ you need 2(x- .5)(x+ 1).
• Jun 26th 2013, 07:27 AM
minneola24
Re: How to do quadratic formula?
Thanks. So if it was 4x^2 as a coefficient I would do the quadratic formula and times it by. 4 in the parenthesis version?
• Jun 26th 2013, 07:36 PM
ibdutt
Re: How to do quadratic formula?
Quote:

Originally Posted by ibdutt
In general for a quadratic equation ax^2 + bx + c = 0 for factorization just write the product of the coefficient of x^2 and constant, in this case ac. Thereafter find such factors of the product ac such that their sum is equal to the coefficient of x. there after split the middle term and group into factors.

in this case your equation is 2x^2 + x - 1
step 1: Product of coefficient of x square 9 in this case = 2 0 and constant term 9 in this case = -1 ) is = -2
step 2. factors of -2 are
-2 = 1x -2 = -1 x 2
step 3. select the factors whose sum is equal to the coefficient of x. in this case 2 + ( -1 ) = 1
step 4. split the middle term with these factors.
2x^2 + 2x - x - 1 = 2x ( x + 1 ) -1 ( x + 1 ) = ( x+1 ) ( 2x - 1)