What are the solutions to the equation -4x^3+6x^2+8=0 ?

The solutions to the equation -4x^3+6x^2+8=0 are x=2,x=-1/4+i(sqrt(15))/4 ,x=-1/4-i(sqrt(15))/4

Find the zeros of -4x^3+6x^2+8=0

The zeros of -4x^3+6x^2+8=0 are x=2,x=-1/4+i(sqrt(15))/4 ,x=-1/4-i(sqrt(15))/4

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- 4 x^{3} + 6 x^{2} + 8 = 0

x = 2, x = - \frac{1}{4} + i \frac{15}{4}, x = - \frac{1}{4} - i \frac{15}{4}

Solution steps

- 4 x^{3} + 6 x^{2} + 8 = 0

Factor

- 4 x^{3} + 6 x^{2} + 8 : - 2 (x - 2) (2 x^{2} + x + 2)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

2 x^{2} + x + 2 = 0 : x = - \frac{1}{4} + i \frac{15}{4}, x = - \frac{1}{4} - i \frac{15}{4}

The solutions are

x = 2, x = - \frac{1}{4} + i \frac{15}{4}, x = - \frac{1}{4} - i \frac{15}{4}

125 t^{4} - 180 t^{3} - 270 t^{2} + 250 = 0

24 x^{3} + 6 x^{2} = 0

y, y - x^{3} = 0

3 x^{4} + 2 x^{2} - 8 = 0

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

What are the solutions to the equation -4x^3+6x^2+8=0 ?
The solutions to the equation -4x^3+6x^2+8=0 are x=2,x=-1/4+i(sqrt(15))/4 ,x=-1/4-i(sqrt(15))/4
Find the zeros of -4x^3+6x^2+8=0
The zeros of -4x^3+6x^2+8=0 are x=2,x=-1/4+i(sqrt(15))/4 ,x=-1/4-i(sqrt(15))/4