quadratic equations

Question

Select the approximate values of x that are solutions to f(x) = 0, where
f(x) = -9x2 + 9x + 9.

 

The four options below are:

{–1.00, 1.00}

{-9, 9}

{–1.00, –1.00}

{–0.62, 1.62}

Answer 1

So the equation you want to solve is -9x2 + 9x + 9 = 0.

 

An easy thing to do to start is to divide through by 9.  That will simplify the numbers.

 

-x2 + x + 1 = 0

 

And then you can also multiply through by -1:

 

x2 - x - 1 = 0

 

Since it's multiple choice, see if there's anything you can eliminate.  Well, option 2 definitely isn't going to work, because 9² and (-9)² are both 81, and that's way bigger than anything you're going to get from the other terms.

 

What about option 1?  Is 1 a solution?  That's easy to calculate, so let's see.  1² - 1 - 1 = -1, so no that doesn't work.  So that rules out option 1.

 

What about option 3?  (-1)² - (-1) - 1 = 1 + 1 -1 = -1 again, so that doesn't work.

 

The only option left is #4.  Try plugging in the numbers to confirm.