select the approximate values of x that are solutions to f(x)=0 where f(x) = -3x^2+2x+6.

Question

select the approximate values of x that are solutions to f(x)=0 where f(x) = -3x^2+2x+6.

If you can also list the steps on how to get the result that would be really helpful as I am stuck and just can't seem to retain the steps or at least grasp the concept.

Answer 1

If Ax² + Bx + C = 0, then, by the Quadratic Formula,     x = -B ± √(B² - 4AC)

                           2A

 

So, for -3x² + 2x + 6 = 0,

 

x = -2 ± √(2² - 4(-3)(6))

                  2(-3)

 

   = -2 ± √76

           -6

 

    = -2 ± 2√19  = 1 ± √19

             -6                 3