What are the solutions to the equation s^5+s^4+4s^3+24s^2+3s+63=0 ?

The solutions to the equation s^5+s^4+4s^3+24s^2+3s+63=0 are s=-3

Find the zeros of s^5+s^4+4s^3+24s^2+3s+63=0

The zeros of s^5+s^4+4s^3+24s^2+3s+63=0 are s=-3

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s^{5} + s^{4} + 4 s^{3} + 24 s^{2} + 3 s + 63 = 0

s = - 3

Solution steps

s^{5} + s^{4} + 4 s^{3} + 24 s^{2} + 3 s + 63 = 0

Factor

s^{5} + s^{4} + 4 s^{3} + 24 s^{2} + 3 s + 63 : (s + 3) (s^{4} - 2 s^{3} + 10 s^{2} - 6 s + 21)

(s + 3) (s^{4} - 2 s^{3} + 10 s^{2} - 6 s + 21) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

s + 3 = 0 or s^{4} - 2 s^{3} + 10 s^{2} - 6 s + 21 = 0

Solve

s + 3 = 0 : s = - 3

Solve

s^{4} - 2 s^{3} + 10 s^{2} - 6 s + 21 = 0 :

No Solution for

s \in R

The solution is

s = - 3

27 x^{5} - 54 x^{4} - 72 x^{3} - 26 x^{2} - 3 x = 0

x^{3} - 7 x + 2 = 0

3 x^{4} - 7 x^{3} - 9 x^{2} + 24 x - 4

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

4 x^{3} - 12 x^{2}

What are the solutions to the equation s^5+s^4+4s^3+24s^2+3s+63=0 ?
The solutions to the equation s^5+s^4+4s^3+24s^2+3s+63=0 are s=-3
Find the zeros of s^5+s^4+4s^3+24s^2+3s+63=0
The zeros of s^5+s^4+4s^3+24s^2+3s+63=0 are s=-3