What are the solutions to the equation s^4+9s^3+32s^2+60s=0 ?

The solutions to the equation s^4+9s^3+32s^2+60s=0 are s=0,s=-5,s=-2+2sqrt(2)i,s=-2-2sqrt(2)i

Find the zeros of s^4+9s^3+32s^2+60s=0

The zeros of s^4+9s^3+32s^2+60s=0 are s=0,s=-5,s=-2+2sqrt(2)i,s=-2-2sqrt(2)i

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s^{4} + 9 s^{3} + 32 s^{2} + 60 s = 0

s = 0, s = - 5, s = - 2 + 22 i, s = - 2 - 22 i

Solution steps

s^{4} + 9 s^{3} + 32 s^{2} + 60 s = 0

Factor

s^{4} + 9 s^{3} + 32 s^{2} + 60 s : s (s + 5) (s^{2} + 4 s + 12)

s (s + 5) (s^{2} + 4 s + 12) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

s = 0 or s + 5 = 0 or s^{2} + 4 s + 12 = 0

Solve

s + 5 = 0 : s = - 5

Solve

s^{2} + 4 s + 12 = 0 : s = - 2 + 22 i, s = - 2 - 22 i

The solutions are

s = 0, s = - 5, s = - 2 + 22 i, s = - 2 - 22 i

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

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

9 x^{4} - 730 x^{2} + 81 = 0

- x^{3} - 12 x^{2} - 43 x - 44 = 0

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

What are the solutions to the equation s^4+9s^3+32s^2+60s=0 ?
The solutions to the equation s^4+9s^3+32s^2+60s=0 are s=0,s=-5,s=-2+2sqrt(2)i,s=-2-2sqrt(2)i
Find the zeros of s^4+9s^3+32s^2+60s=0
The zeros of s^4+9s^3+32s^2+60s=0 are s=0,s=-5,s=-2+2sqrt(2)i,s=-2-2sqrt(2)i