What are the solutions to the equation s^4-10s^3-5s^2=0 ?

The solutions to the equation s^4-10s^3-5s^2=0 are s=0,s=5+sqrt(30),s=5-sqrt(30)

Find the zeros of s^4-10s^3-5s^2=0

The zeros of s^4-10s^3-5s^2=0 are s=0,s=5+sqrt(30),s=5-sqrt(30)

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s^{4} - 10 s^{3} - 5 s^{2} = 0

s = 0, s = 5 + 30, s = 5 - 30

Decimal Notation

s = 0, s = 10.47722 \dots, s = - 0.47722 \dots

Solution steps

s^{4} - 10 s^{3} - 5 s^{2} = 0

Factor

s^{4} - 10 s^{3} - 5 s^{2} : s^{2} (s^{2} - 10 s - 5)

s^{2} (s^{2} - 10 s - 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

s = 0 or s^{2} - 10 s - 5 = 0

Solve

s^{2} - 10 s - 5 = 0 : s = 5 + 30, s = 5 - 30

The solutions are

s = 0, s = 5 + 30, s = 5 - 30

x, x^{4} - 81 = 0

v^{10} - 6 v = - 104

6 x^{5} + 20 x^{3} = 23 x^{4}

x^{7} + 1 = 0

x^{6} + 9 x^{3} - 5 = 0

What are the solutions to the equation s^4-10s^3-5s^2=0 ?
The solutions to the equation s^4-10s^3-5s^2=0 are s=0,s=5+sqrt(30),s=5-sqrt(30)
Find the zeros of s^4-10s^3-5s^2=0
The zeros of s^4-10s^3-5s^2=0 are s=0,s=5+sqrt(30),s=5-sqrt(30)