What are the solutions to the equation x^4+9x^3+12x^2-34x+12=0 ?

The solutions to the equation x^4+9x^3+12x^2-34x+12=0 are x=1,x=-6,x=-2+sqrt(6),x=-2-sqrt(6)

Find the zeros of x^4+9x^3+12x^2-34x+12=0

The zeros of x^4+9x^3+12x^2-34x+12=0 are x=1,x=-6,x=-2+sqrt(6),x=-2-sqrt(6)

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x^{4} + 9 x^{3} + 12 x^{2} - 34 x + 12 = 0

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

Decimal Notation

x = 1, x = - 6, x = 0.44948 \dots, x = - 4.44948 \dots

Solution steps

x^{4} + 9 x^{3} + 12 x^{2} - 34 x + 12 = 0

Factor

x^{4} + 9 x^{3} + 12 x^{2} - 34 x + 12 : (x - 1) (x + 6) (x^{2} + 4 x - 2)

(x - 1) (x + 6) (x^{2} + 4 x - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x + 6 = 0 or x^{2} + 4 x - 2 = 0

Solve

x - 1 = 0 : x = 1

Solve

x + 6 = 0 : x = - 6

Solve

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

The solutions are

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

r^{4} - 2 r^{3} + r^{2} + 2 r - 2 = 0

3 x^{3} - 81 = 0

6 y^{2} + 2 y - 5 y^{4} = 0

x^{3} - 594 x + 3186 = 0

2 x^{3} + 6 x = 0

What are the solutions to the equation x^4+9x^3+12x^2-34x+12=0 ?
The solutions to the equation x^4+9x^3+12x^2-34x+12=0 are x=1,x=-6,x=-2+sqrt(6),x=-2-sqrt(6)
Find the zeros of x^4+9x^3+12x^2-34x+12=0
The zeros of x^4+9x^3+12x^2-34x+12=0 are x=1,x=-6,x=-2+sqrt(6),x=-2-sqrt(6)