Español | Português
  1. Home
  2. Calculators
  3. Calculators: Algebra II
  4. Pre-Calculus Calculator

Roots of $$$f{\left(x \right)} = x^{4} + 2 x^{3} - 3 x^{2} - 4 x + 12$$$

The calculator will try to find all roots of the polynomial $$$f{\left(x \right)} = x^{4} + 2 x^{3} - 3 x^{2} - 4 x + 12$$$.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Your Input

Solve $$$x^{4} + 2 x^{3} - 3 x^{2} - 4 x + 12 = 0$$$.

Answer

Root: $$$- \frac{1}{2} - \frac{\sqrt{9 - 8 \sqrt{2} i}}{2}\approx -2.212338762292707 + 0.825895899523735 i$$$A, multiplicity: $$$1$$$A.

Root: $$$- \frac{1}{2} + \frac{\sqrt{9 - 8 \sqrt{2} i}}{2}\approx 1.212338762292707 - 0.825895899523735 i$$$A, multiplicity: $$$1$$$A.

Root: $$$- \frac{1}{2} - \frac{\sqrt{9 + 8 \sqrt{2} i}}{2}\approx -2.212338762292707 - 0.825895899523735 i$$$A, multiplicity: $$$1$$$A.

Root: $$$- \frac{1}{2} + \frac{\sqrt{9 + 8 \sqrt{2} i}}{2}\approx 1.212338762292707 + 0.825895899523735 i$$$A, multiplicity: $$$1$$$A.