What are the solutions to the equation 3x^3+4x^2+5x-6=0 ?

The solutions to the equation 3x^3+4x^2+5x-6=0 are x= 2/3 ,x=-1+sqrt(2)i,x=-1-sqrt(2)i

Find the zeros of 3x^3+4x^2+5x-6=0

The zeros of 3x^3+4x^2+5x-6=0 are x= 2/3 ,x=-1+sqrt(2)i,x=-1-sqrt(2)i

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3 x^{3} + 4 x^{2} + 5 x - 6 = 0

x = \frac{2}{3}, x = - 1 + 2 i, x = - 1 - 2 i

Solution steps

3 x^{3} + 4 x^{2} + 5 x - 6 = 0

Factor

3 x^{3} + 4 x^{2} + 5 x - 6 : (3 x - 2) (x^{2} + 2 x + 3)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

3 x - 2 = 0 : x = \frac{2}{3}

Solve

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

The solutions are

x = \frac{2}{3}, x = - 1 + 2 i, x = - 1 - 2 i

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

3 x^{4} + 4 x^{3} - 12 x^{2} + 10 = 0

(x) = x^{3} - 3 x^{2} - 9 x - 5

x, x^{2} + (y - c b r t (x^{2}))^{2} = 25

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

What are the solutions to the equation 3x^3+4x^2+5x-6=0 ?
The solutions to the equation 3x^3+4x^2+5x-6=0 are x= 2/3 ,x=-1+sqrt(2)i,x=-1-sqrt(2)i
Find the zeros of 3x^3+4x^2+5x-6=0
The zeros of 3x^3+4x^2+5x-6=0 are x= 2/3 ,x=-1+sqrt(2)i,x=-1-sqrt(2)i