What are the solutions to the equation d^5+27d^2=0 ?

The solutions to the equation d^5+27d^2=0 are d=0,d=-3,d= 3/2-(3sqrt(3))/2 i,d= 3/2+(3sqrt(3))/2 i

Find the zeros of d^5+27d^2=0

The zeros of d^5+27d^2=0 are d=0,d=-3,d= 3/2-(3sqrt(3))/2 i,d= 3/2+(3sqrt(3))/2 i

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d^{5} + 27 d^{2} = 0

d = 0, d = - 3, d = \frac{3}{2} - \frac{3 3}{2} i, d = \frac{3}{2} + \frac{3 3}{2} i

Solution steps

d^{5} + 27 d^{2} = 0

Factor

d^{5} + 27 d^{2} : d^{2} (d^{3} + 27)

d^{2} (d^{3} + 27) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

d = 0 or d^{3} + 27 = 0

Solve

d^{3} + 27 = 0 : d = - 3, d = \frac{3}{2} - \frac{3 3}{2} i, d = \frac{3}{2} + \frac{3 3}{2} i

The solutions are

d = 0, d = - 3, d = \frac{3}{2} - \frac{3 3}{2} i, d = \frac{3}{2} + \frac{3 3}{2} i

40 x^{3} - 36 x^{2} - 14 = 0

4 x^{4} = 18 x^{2}

x^{4} - x^{3} - x + 1 = 0

3 x^{3} + 2 x - 1 = 8 x^{2} - 4

18 x^{3} + 90 x + 55 = 0

What are the solutions to the equation d^5+27d^2=0 ?
The solutions to the equation d^5+27d^2=0 are d=0,d=-3,d= 3/2-(3sqrt(3))/2 i,d= 3/2+(3sqrt(3))/2 i
Find the zeros of d^5+27d^2=0
The zeros of d^5+27d^2=0 are d=0,d=-3,d= 3/2-(3sqrt(3))/2 i,d= 3/2+(3sqrt(3))/2 i