What are the solutions to the equation a^3+5a+6=0 ?

The solutions to the equation a^3+5a+6=0 are a=-1,a= 1/2+i(sqrt(23))/2 ,a= 1/2-i(sqrt(23))/2

Find the zeros of a^3+5a+6=0

The zeros of a^3+5a+6=0 are a=-1,a= 1/2+i(sqrt(23))/2 ,a= 1/2-i(sqrt(23))/2

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a^{3} + 5 a + 6 = 0

a = - 1, a = \frac{1}{2} + i \frac{23}{2}, a = \frac{1}{2} - i \frac{23}{2}

Solution steps

a^{3} + 5 a + 6 = 0

Factor

a^{3} + 5 a + 6 : (a + 1) (a^{2} - a + 6)

(a + 1) (a^{2} - a + 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

a + 1 = 0 or a^{2} - a + 6 = 0

Solve

a + 1 = 0 : a = - 1

Solve

a^{2} - a + 6 = 0 : a = \frac{1}{2} + i \frac{23}{2}, a = \frac{1}{2} - i \frac{23}{2}

The solutions are

a = - 1, a = \frac{1}{2} + i \frac{23}{2}, a = \frac{1}{2} - i \frac{23}{2}

x^{5} - 243 = 0

x^{3} - 13 x^{2} + 23 x - 11 = 0

x^{3} + 2 x^{2} - 16 x - 32

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

(x + 4) (x^{2} - x + 3) = 0

What are the solutions to the equation a^3+5a+6=0 ?
The solutions to the equation a^3+5a+6=0 are a=-1,a= 1/2+i(sqrt(23))/2 ,a= 1/2-i(sqrt(23))/2
Find the zeros of a^3+5a+6=0
The zeros of a^3+5a+6=0 are a=-1,a= 1/2+i(sqrt(23))/2 ,a= 1/2-i(sqrt(23))/2