What are the solutions to the equation 2x^3-3x^2+16x-24=0 ?

The solutions to the equation 2x^3-3x^2+16x-24=0 are x= 3/2 ,x=2sqrt(2)i,x=-2sqrt(2)i

Find the zeros of 2x^3-3x^2+16x-24=0

The zeros of 2x^3-3x^2+16x-24=0 are x= 3/2 ,x=2sqrt(2)i,x=-2sqrt(2)i

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2 x^{3} - 3 x^{2} + 16 x - 24 = 0

x = \frac{3}{2}, x = 22 i, x = - 22 i

Solution steps

2 x^{3} - 3 x^{2} + 16 x - 24 = 0

Factor

2 x^{3} - 3 x^{2} + 16 x - 24 : (2 x - 3) (x^{2} + 8)

(2 x - 3) (x^{2} + 8) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Solve

x^{2} + 8 = 0 : x = 22 i, x = - 22 i

The solutions are

x = \frac{3}{2}, x = 22 i, x = - 22 i

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

x^{4} + 4 x^{2} - 32 = 0

- a^{3} + 4 a^{2} - 3 a = 0

12 x^{5} - 8 x^{4} - 12 x + 8 = 0

2 x^{3} + x = 4

What are the solutions to the equation 2x^3-3x^2+16x-24=0 ?
The solutions to the equation 2x^3-3x^2+16x-24=0 are x= 3/2 ,x=2sqrt(2)i,x=-2sqrt(2)i
Find the zeros of 2x^3-3x^2+16x-24=0
The zeros of 2x^3-3x^2+16x-24=0 are x= 3/2 ,x=2sqrt(2)i,x=-2sqrt(2)i