Question

Solve the equation:
x^3+3x^2-x+12=0 Please help!!

Answer 1

`x=-4,(1\pm√(11)i)/(2)`

Explanation:

The synthetic division shown below both confirms that x=-4 is a solution and gives the reduced quadratic as

x^2 -x +3 = 0

Using the quadratic formula with a=1, b=-1, c=3, we find the other two solutions to be ...

`x=(-(-1)\pm√((-1)^2-4(1)(3)))/(2(1))=(1\pm√(-11))/(2)\\\\x=(1\pm√(11)i)/(2)`

____

The graph of the cubic shows it has one real root at x=-4. Dividing the function by the corresponding factor shows the quadratic factor to have its vertex at (0.5, 2.75). This means the remaining roots are 0.5±i√2.75, matching the above result.