find-the-root-of-x-4-4x-3-11x-2-14x-30-0-

Question Number 172025 by Mikenice last updated on 23/Jun/22

f i n d t h e r o o t o f

x^{4} + 4 x^{3} + 11 x^{2} + 14 x - 30 = 0 .

Answered by thfchristopher last updated on 23/Jun/22

x^{4} + 4 x^{3} + 11 x^{2} + 14 x - 30 = 0

\Rightarrow (x - 1) (x^{3} + 5 x^{2} + 16 x + 30) = 0

\Rightarrow (x - 1) (x + 3) (x^{2} + 2 x + 10) = 0

\Rightarrow (x - 1) (x + 3) (x + 1 + 3 i) (x + 1 - 3 i) = 0

∴ x = 1, - 3, - 1 \pm 3 i