What are the solutions to the equation 5x^3-12x^2+19x-6=0 ?

The solutions to the equation 5x^3-12x^2+19x-6=0 are x= 2/5 ,x=1+sqrt(2)i,x=1-sqrt(2)i

Find the zeros of 5x^3-12x^2+19x-6=0

The zeros of 5x^3-12x^2+19x-6=0 are x= 2/5 ,x=1+sqrt(2)i,x=1-sqrt(2)i

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5 x^{3} - 12 x^{2} + 19 x - 6 = 0

x = \frac{2}{5}, x = 1 + 2 i, x = 1 - 2 i

Solution steps

5 x^{3} - 12 x^{2} + 19 x - 6 = 0

Factor

5 x^{3} - 12 x^{2} + 19 x - 6 : (5 x - 2) (x^{2} - 2 x + 3)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

5 x - 2 = 0 : x = \frac{2}{5}

Solve

x^{2} - 2 x + 3 = 0 : x = 1 + 2 i, x = 1 - 2 i

The solutions are

x = \frac{2}{5}, x = 1 + 2 i, x = 1 - 2 i

x^{3} + 3 x^{2} - 4 x - 12

a x^{3}

m^{3} - 3 m^{2} + 2 m - 6 = 0

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

7 x^{3} = 189

What are the solutions to the equation 5x^3-12x^2+19x-6=0 ?
The solutions to the equation 5x^3-12x^2+19x-6=0 are x= 2/5 ,x=1+sqrt(2)i,x=1-sqrt(2)i
Find the zeros of 5x^3-12x^2+19x-6=0
The zeros of 5x^3-12x^2+19x-6=0 are x= 2/5 ,x=1+sqrt(2)i,x=1-sqrt(2)i