What are the solutions to the equation p^3+2p+3=0 ?

The solutions to the equation p^3+2p+3=0 are p=-1,p= 1/2+i(sqrt(11))/2 ,p= 1/2-i(sqrt(11))/2

Find the zeros of p^3+2p+3=0

The zeros of p^3+2p+3=0 are p=-1,p= 1/2+i(sqrt(11))/2 ,p= 1/2-i(sqrt(11))/2

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p^{3} + 2 p + 3 = 0

p = - 1, p = \frac{1}{2} + i \frac{11}{2}, p = \frac{1}{2} - i \frac{11}{2}

Solution steps

p^{3} + 2 p + 3 = 0

Factor

p^{3} + 2 p + 3 : (p + 1) (p^{2} - p + 3)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

p + 1 = 0 or p^{2} - p + 3 = 0

Solve

p + 1 = 0 : p = - 1

Solve

p^{2} - p + 3 = 0 : p = \frac{1}{2} + i \frac{11}{2}, p = \frac{1}{2} - i \frac{11}{2}

The solutions are

p = - 1, p = \frac{1}{2} + i \frac{11}{2}, p = \frac{1}{2} - i \frac{11}{2}

x^{4} = \frac{16}{9}

x, 729 x^{6} - 4096 = 0

k, k^{3} - 4 k^{2} + k + 6 = 0

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

f^{6} = 6 + 3

What are the solutions to the equation p^3+2p+3=0 ?
The solutions to the equation p^3+2p+3=0 are p=-1,p= 1/2+i(sqrt(11))/2 ,p= 1/2-i(sqrt(11))/2
Find the zeros of p^3+2p+3=0
The zeros of p^3+2p+3=0 are p=-1,p= 1/2+i(sqrt(11))/2 ,p= 1/2-i(sqrt(11))/2