f(x)=0, where f(x)=-3x^2+2x+8

Question

What is the approximate value of x

Answer 1

Felicia, this is asking for a value of x if -3x² + 2x + 8 = 0

 

To factor, we need to multiply the first and third coefficients.  -3 x 8 = -24

 

We need to find two factors of -24 that equal 2 (the middle coefficient) when added.

 

6 and -4? Check!

 

We are going to split 2x into 6x - 4x

 

-3x² + 6x - 4x + 8 = 0

 

What's in common between the first two terms?  -3x, right?  -3x(x - 2)

 

What's in common between the last two terms?  -4, right?  -4(x - 2)

 

Since what is inside the two sets of parentheses after factoring out something is the same (x - 2), we can combine what's outside both into their own parentheses.

 

(-3x -  4)(x - 2) = 0

 

For the right to be 0, then either of the left have to equal 0.

 

-3x - 4 = 0

     -3x = 4

        x = -4/3 = - 1 1/3

 

x - 2 = 0

     x = 2

 

So, we have x = 2 and x = -1 1/13

 

Hope this helps!