Using the formula method solve: z^2-12x+12=0

Solving    -x2+12x+12 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     -1

                     B   =    12

                     C   =   12

Accordingly,  B2  -  4AC   =

                    144 - (-48) =

                    192

Applying the quadratic formula :

              -12 ± √ 192

  x  =    ——————

                     -2

Can  √ 192 be simplified ?

Yes!   The prime factorization of  192   is

  2•2•2•2•2•2•3  

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 192   =  √ 2•2•2•2•2•2•3   =2•2•2•√ 3   =

               ±  8 • √ 3

 √ 3   , rounded to 4 decimal digits, is   1.7321

So now we are looking at:

          x  =  ( -12 ± 8 •  1.732 ) / -2

Two real solutions:

x =(-12+√192)/-2=6-4√ 3 = -0.928

or:

x =(-12-√192)/-2=6+4√ 3 = 12.928

x =(-12-√192)/-2=6+4√ 3 = 12.928

x =(-12+√192)/-2=6-4√ 3 = -0.928

These are the two solutions

Hope my answer helps!

answer: expected value of x = 1.0

step-by-step explanation:

p(x=0) = 0.25

p(x=1) = 0.50

p(x=2) = 0.25

expected value for x = 0×0.25 + 1×0.5 + 2×0.25 = 1.0