What are the solutions to the equation 8a^3-12a^2+6a+215=0 ?

The solutions to the equation 8a^3-12a^2+6a+215=0 are a=-5/2 ,a=2+i(3sqrt(3))/2 ,a=2-i(3sqrt(3))/2

Find the zeros of 8a^3-12a^2+6a+215=0

The zeros of 8a^3-12a^2+6a+215=0 are a=-5/2 ,a=2+i(3sqrt(3))/2 ,a=2-i(3sqrt(3))/2

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8 a^{3} - 12 a^{2} + 6 a + 215 = 0

a = - \frac{5}{2}, a = 2 + i \frac{3 3}{2}, a = 2 - i \frac{3 3}{2}

Solution steps

8 a^{3} - 12 a^{2} + 6 a + 215 = 0

Factor

8 a^{3} - 12 a^{2} + 6 a + 215 : (2 a + 5) (4 a^{2} - 16 a + 43)

(2 a + 5) (4 a^{2} - 16 a + 43) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 a + 5 = 0 or 4 a^{2} - 16 a + 43 = 0

Solve

2 a + 5 = 0 : a = - \frac{5}{2}

Solve

4 a^{2} - 16 a + 43 = 0 : a = 2 + i \frac{3 3}{2}, a = 2 - i \frac{3 3}{2}

The solutions are

a = - \frac{5}{2}, a = 2 + i \frac{3 3}{2}, a = 2 - i \frac{3 3}{2}

9 x^{4} - 3 x^{3} + 34 x^{2} - 12 x - 8 = 0

a^{3} - 44 a + 48 = 0

x^{3} + x = 0

x + x^{3} = 0

(x + 1)^{3} = 64

What are the solutions to the equation 8a^3-12a^2+6a+215=0 ?
The solutions to the equation 8a^3-12a^2+6a+215=0 are a=-5/2 ,a=2+i(3sqrt(3))/2 ,a=2-i(3sqrt(3))/2
Find the zeros of 8a^3-12a^2+6a+215=0
The zeros of 8a^3-12a^2+6a+215=0 are a=-5/2 ,a=2+i(3sqrt(3))/2 ,a=2-i(3sqrt(3))/2