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

The solutions to the equation 2x^3-x^2-12=0 are x=2,x=-3/4+i(sqrt(39))/4 ,x=-3/4-i(sqrt(39))/4

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

The zeros of 2x^3-x^2-12=0 are x=2,x=-3/4+i(sqrt(39))/4 ,x=-3/4-i(sqrt(39))/4

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2 x^{3} - x^{2} - 12 = 0

x = 2, x = - \frac{3}{4} + i \frac{39}{4}, x = - \frac{3}{4} - i \frac{39}{4}

Solution steps

2 x^{3} - x^{2} - 12 = 0

Factor

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

(x - 2) (2 x^{2} + 3 x + 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or 2 x^{2} + 3 x + 6 = 0

Solve

x - 2 = 0 : x = 2

Solve

2 x^{2} + 3 x + 6 = 0 : x = - \frac{3}{4} + i \frac{39}{4}, x = - \frac{3}{4} - i \frac{39}{4}

The solutions are

x = 2, x = - \frac{3}{4} + i \frac{39}{4}, x = - \frac{3}{4} - i \frac{39}{4}

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

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

(x^{2} - 1) \cdot (5 - x) = 0

(x^{2} + 2 x)^{2} - 5 (x^{2} + 2 x) + 6 = 0

a, a^{4} b + 2 c^{5} = d^{1} e

What are the solutions to the equation 2x^3-x^2-12=0 ?
The solutions to the equation 2x^3-x^2-12=0 are x=2,x=-3/4+i(sqrt(39))/4 ,x=-3/4-i(sqrt(39))/4
Find the zeros of 2x^3-x^2-12=0
The zeros of 2x^3-x^2-12=0 are x=2,x=-3/4+i(sqrt(39))/4 ,x=-3/4-i(sqrt(39))/4