SOLUTION: It is given that -2 is one of the roots of the quadratic equation h - 8x - 2x² = 0. Find the value of h.

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Question 421955: It is given that -2 is one of the roots of the quadratic equation
h - 8x - 2x² = 0. Find the value of h.
Found 3 solutions by MathLover1, solver91311, Edwin McCravy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

It is given that -2 is one of the roots x of the quadratic equation

x=-2
h-8x-2x%5E2=0........plug in x=-2 and solve for h
h-8%28-2%29-2%28-2%29%5E2=0
h%2B16-2%284%29=0
h%2B16-8=0
h%2B8=0
h=-8



Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Two ways to do this.

Use synthetic division.

















So





Alternatively, use the quadratic formula:





Hence



So





Same result.

John

My calculator said it, I believe it, that settles it
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Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
It is given that -2 is one of the roots of the quadratic equation
h - 8x - 2x² = 0. Find the value of h.


We get the left side into the form of a "monic trinomial"

x² + Bx + C = 0

and use the theorem that B is the opposite of the sum of 
the roots and C is the product of the roots.

h - 8x - 2x² = 0

We rearrange the left side in descending order:

-2x² - 8x + h = 0

Then we divide every term by -2

-2x²    8x     h     0
———— - ———— + ——— = ———
 -2     -2    -2    -2
               h 
    x² + 4x - ——— = 0
               2

We first determine the other zero by using the fact that
the coefficient of x, which is +4 is the sum of the roots with
the opposite sign.  If the roots are r1 and r2,
then  

r1 + r2 = -4  (which is +4 with the opposite sign).

We are told that r1 = -2, so we substitute that and get:

-2 + r2 = -4
     r2 = -2

So both roots are the same.  Now the last term of the "monic trinomial"
is the product of the roots, therefore

               h 
            - ——— = (-2)(-2)
               2

               h 
            - ——— = 4
               2

               -h = 8

                h = -8.

Checking:

  h - 8x - 2x² = 0
 
 -8 - 8x - 2x² = 0

 -2x² - 8x - 8 = 0

   x² + 4x + 4 = 0

(x + 2)(x + 2) = 0

x + 2 =  0;  x + 2 =  0
    x = -2;      x = -2 

So it checks. h = -8

Edwin