Question

Determine the roots or zeros of the equation

Answer 1

Determining the zeros means that you are looking for the x-intercept of the function....

You can factor this function ....

QUADRATIC FORMULA : ax^2 + bx + c

f(x) = - 8 x^2 + 2x + 1

Set f(x) to 0 and factor the expression....

0  = - 8 x^2 + 2x + 1

Get everything to the left side... because variables have to be on the left side

8x^2 - 2x - 1 = 0

Now factor...  a = 8 , b = -2 , c = - 1

To factor... Start by multiplying a * c =>    8 *  -1 => - 8 

Now you have to find two numbers that multiply to -8 and add up to b which is -2 

We could use - 4 and 2 because...   - 4 * 2 = - 8 
                                                          - 4 + 2 = - 2 

Now you rewrite the expression....

8x^2 - 4x + 2x - 1

Now take out common factors...

4x ( 2x - 1 ) + 1 ( 2x - 1 ) 

( 2x - 1 ) ( 4x + 1 ) 

Now you have to write two separate equations and solve for x...

( 2 x - 1 )                                                  ( 4x  + 1 )
 
2x - 1 = 0                                                   4x + 1 = 0 

Add one to both sides..                            Subtract 1 from both sides...

2x = 1                                                            4x = - 1 

Divide by 2 to x by its self...                            Divide by 4

x = 1/2                                                            x = - 1/4

The zeros of f(x) = - 8 x^2 + 2x + 1 are 1/2 and -1/4