SOLUTION: 2. If x = 1 and x = -8, then form a quadratic equation

Algebra ->  Graphs -> SOLUTION: 2. If x = 1 and x = -8, then form a quadratic equation      Log On


   

Question 155167: 2. If x = 1 and x = -8, then form a quadratic equation
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given zeros

x=1 and x=-8


Get all terms to the left side in each case (ie subtract 1 from both sides in the first equation and add 8 to both sides in the second equation)


x-1=0 and x%2B8=0


Now use the zero product property in reverse to join the factors.


%28x-1%29%28x%2B8%29=0


FOIL and multiply


x%5E2%2B7x-8=0


-------------------------------------------
Answer:

So the polynomial with zeros of x=1 and x=-8 is

x%5E2%2B7%2Ax-8



Notice how if we graph y=x%5E2%2B7%2Ax-8, we can see that the polynomial has roots of x=1 and x=-8

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2B7%2Ax-8+%29+ Graph of y=x%5E2%2B7%2Ax-8 with roots of x=1 and x=-8