What are the solutions to the equation x^3-6x^2+13x-12=0 ?

The solutions to the equation x^3-6x^2+13x-12=0 are x=3,x= 3/2+i(sqrt(7))/2 ,x= 3/2-i(sqrt(7))/2

Find the zeros of x^3-6x^2+13x-12=0

The zeros of x^3-6x^2+13x-12=0 are x=3,x= 3/2+i(sqrt(7))/2 ,x= 3/2-i(sqrt(7))/2

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x^{3} - 6 x^{2} + 13 x - 12 = 0

x = 3, x = \frac{3}{2} + i \frac{7}{2}, x = \frac{3}{2} - i \frac{7}{2}

Solution steps

x^{3} - 6 x^{2} + 13 x - 12 = 0

Factor

x^{3} - 6 x^{2} + 13 x - 12 : (x - 3) (x^{2} - 3 x + 4)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 3 = 0 : x = 3

Solve

x^{2} - 3 x + 4 = 0 : x = \frac{3}{2} + i \frac{7}{2}, x = \frac{3}{2} - i \frac{7}{2}

The solutions are

x = 3, x = \frac{3}{2} + i \frac{7}{2}, x = \frac{3}{2} - i \frac{7}{2}

x^{2} - 5 x = 2 x^{3} - 4 x^{2} - x + 6

1200 = 600 x^{2} (3 - x)

x^{4} - 3 x^{2} = 10

w^{3} = 5

2 x^{4} + x^{3} - 7 x^{2} - 3 x + 3 = 0

What are the solutions to the equation x^3-6x^2+13x-12=0 ?
The solutions to the equation x^3-6x^2+13x-12=0 are x=3,x= 3/2+i(sqrt(7))/2 ,x= 3/2-i(sqrt(7))/2
Find the zeros of x^3-6x^2+13x-12=0
The zeros of x^3-6x^2+13x-12=0 are x=3,x= 3/2+i(sqrt(7))/2 ,x= 3/2-i(sqrt(7))/2