Solving quadratic functions with equations

Tutors, sign in to answer this question.

Tom D. | Very patient Math Expert who likes to teachVery patient Math Expert who likes to te...

Hi Raven,

2n^2 + 4n -16 = 0

This is standard form aN^2 + bN + c (a=2,b=4,c= -16)

1)examine the possible factors of the a & c constants [ c=(-2)(8) or (2)(-8) or (4)(-4) or (1)(-16) or (-1)(16) ]

[a = (1)(2) ]

2)look at the possible combinations and try to construct the 'b' constant from the candidate factors. For example consider the form

(2n + Q)(n + R)

QR = c = -16

(Q + 2R) = b = 4

After a little study, you'll see that (Q=8 , R=-2) yields the correct 'b' So we FOUND the solution just by examination. This doesn't work all the time, but is faster if the roots are simple

(2n + 8)(n - 2)-----> n=-4, n=2 are the solutions

2)If you cannot find simple factors, you are left with the quadratic formula which always provides the correct answer: n = [ -b ± sqrt(b^2 - 4ac) ]/2a

n= [ -4 ± sqrt(16 - 4(2)(-16) ]/2(2)

n= -1 ± sqrt(16 + 128)/4

n= -1 ± sqrt(144)/4 (sqrt(144)=12)

n= -1 ± 3

n= -4, 2 (Same as we got above)

Hi Raven;

2n^{2}+4n-16=0

For the FOIL...

FIRST must be (2x)(n)=2n^{2}.

OUTER and INNER must add-up to 4n.

LAST must be (16)(1) or (1)(16) or (8)(2) or (2)(8) or (4)(4) and one number must be negative to produce -16.

(2n+8)(n-2)=0

Let's FOIL...

FIRST...(2n)(n)=2n^{2}

OUTER...(2n)(-2)=-4n

INNER...(8)(n)=8n

LAST...(8)(-2)=-16

2n^{2}-4n+8n-16=0

2n^{2}+4n-16=0

(2n+8)(n-2)=0

Either or both parenthetical equations must equal zero.

2n+8=0

2n=-8

n=-4

n-2=0

n=2

First, divide both sides by 2. You will get:

n^{2}+2n-8=0

Now either factor out or use quadratic formula.

1) Factoring.

Product of roots shall be equal to -8. Sum of them equals to -2. Obvious choice is -4 and 2. (-4)*2=-8, -4+2=-2.

So we have the following factoring: (n+4)(n-2)=0. This means that either n=2 or n=-4.

2) Quadratic formula.

n_{1,2}={-2±√[(-2)^{2}-4*1*(-8)]}/2

n_{1}=[-2+√36]/2=(-2+6)/2=2

n_{2}=[-2-√36]/2=(-2-6)/2=-4

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

## Comments

equation, not quadraticformula. The second thing, you shall think generally, not in specifics. If I write yx^{2}+zx+s=0, this is still quadratic equation. And m*sin^{2}(x)+h*sin(x)+w=0 is quadratic equation, with respect to sin(x), of course.notan even times an odd !