What are the solutions to the equation 10x+0.5x^2-0.001x^3-5000=0 ?

The solutions to the equation 10x+0.5x^2-0.001x^3-5000=0 are x=500,x=-100,x=100

Find the zeros of 10x+0.5x^2-0.001x^3-5000=0

The zeros of 10x+0.5x^2-0.001x^3-5000=0 are x=500,x=-100,x=100

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10 x + 0.5 x^{2} - 0.001 x^{3} - 5000 = 0

x = 500, x = - 100, x = 100

Solution steps

10 x + 0.5 x^{2} - 0.001 x^{3} - 5000 = 0

Multiply both sides by

1000

10000 x + 500 x^{2} - x^{3} - 5000000 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- x^{3} + 500 x^{2} + 10000 x - 5000000 = 0

Factor

- x^{3} + 500 x^{2} + 10000 x - 5000000 : - (x - 500) (x + 100) (x - 100)

- (x - 500) (x + 100) (x - 100) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 500 = 0 or x + 100 = 0 or x - 100 = 0

Solve

x - 500 = 0 : x = 500

Solve

x + 100 = 0 : x = - 100

Solve

x - 100 = 0 : x = 100

The solutions are

x = 500, x = - 100, x = 100

x^{4} - x^{2} = 7 x^{2} + 9

- x^{3} + 4 x^{2} - 9 x - 6

12 x^{3} - 20 x^{2} + x + 3

0 = 12 t^{3} - 48 t^{2} + 48 t

24 x^{3} - 3 = 0

What are the solutions to the equation 10x+0.5x^2-0.001x^3-5000=0 ?
The solutions to the equation 10x+0.5x^2-0.001x^3-5000=0 are x=500,x=-100,x=100
Find the zeros of 10x+0.5x^2-0.001x^3-5000=0
The zeros of 10x+0.5x^2-0.001x^3-5000=0 are x=500,x=-100,x=100