What are the solutions to the equation x^4-6x^3+9x^2+4x-12=0 ?

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

Find the zeros of x^4-6x^3+9x^2+4x-12=0

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

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x^{4} - 6 x^{3} + 9 x^{2} + 4 x - 12 = 0

x = - 1, x = 2, x = 3

Solution steps

x^{4} - 6 x^{3} + 9 x^{2} + 4 x - 12 = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x - 2 = 0 or x - 3 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x - 2 = 0 : x = 2

Solve

x - 3 = 0 : x = 3

The solutions are

x = - 1, x = 2, x = 3

y, x^{3} = y^{3}

x^{4} - x^{2} + 4 = 0

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

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

y, y^{4} = x

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