What are the solutions to the equation x^4+6x^3+3x^2-16x+6=0 ?

The solutions to the equation x^4+6x^3+3x^2-16x+6=0 are x=1,x=-3,x=-2+sqrt(6),x=-2-sqrt(6)

Find the zeros of x^4+6x^3+3x^2-16x+6=0

The zeros of x^4+6x^3+3x^2-16x+6=0 are x=1,x=-3,x=-2+sqrt(6),x=-2-sqrt(6)

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x^{4} + 6 x^{3} + 3 x^{2} - 16 x + 6 = 0

x = 1, x = - 3, x = - 2 + 6, x = - 2 - 6

Decimal Notation

x = 1, x = - 3, x = 0.44948 \dots, x = - 4.44948 \dots

Solution steps

x^{4} + 6 x^{3} + 3 x^{2} - 16 x + 6 = 0

Factor

x^{4} + 6 x^{3} + 3 x^{2} - 16 x + 6 : (x - 1) (x + 3) (x^{2} + 4 x - 2)

(x - 1) (x + 3) (x^{2} + 4 x - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x + 3 = 0 or x^{2} + 4 x - 2 = 0

Solve

x - 1 = 0 : x = 1

Solve

x + 3 = 0 : x = - 3

Solve

x^{2} + 4 x - 2 = 0 : x = - 2 + 6, x = - 2 - 6

The solutions are

x = 1, x = - 3, x = - 2 + 6, x = - 2 - 6

- x^{3} - 6 x^{2} - 12 x - 8 = 0

x^{3} + 5 x^{2} - 6 x = 0

2 (x + 6) (x^{2} + 36) = 0

x^{5} + 2 x - 2 = 0

- x^{3} + 5 x^{2} - 3 x = 1

What are the solutions to the equation x^4+6x^3+3x^2-16x+6=0 ?
The solutions to the equation x^4+6x^3+3x^2-16x+6=0 are x=1,x=-3,x=-2+sqrt(6),x=-2-sqrt(6)
Find the zeros of x^4+6x^3+3x^2-16x+6=0
The zeros of x^4+6x^3+3x^2-16x+6=0 are x=1,x=-3,x=-2+sqrt(6),x=-2-sqrt(6)