what are the possible solutions to the equation x^3-2.341x^2-6.759x+9.724=0

Question

I know there is one negative answer and two positive answers. I am to use the goalseek function in excel to find these answers but I can only get this function to give me one of the correct answers (1.19629).

Answer 1

You have one solution x=1.19629. To find the other two solutions divide the cubic by x-1.19629 to produce a quadratic and use the quadratic formula to solve it. Using synthetic divison we have

1.19629 | 1 -2.341     -6.759          9.724

                1  1.19629 -1.369405 | -9.724

                1 -1.14471 -8.128405 |     0     = x²-1.14471x-8.128405.

a=1, b=-1.14471, c=-8.128405, x=(-b±√(b²-4ac))/2a=3.48027 or -2.33557.