What are the solutions to the equation x^3-30x^2+15^3=0 ?

The solutions to the equation x^3-30x^2+15^3=0 are x=15,x=(15+15sqrt(5))/2 ,x=(15-15sqrt(5))/2

Find the zeros of x^3-30x^2+15^3=0

The zeros of x^3-30x^2+15^3=0 are x=15,x=(15+15sqrt(5))/2 ,x=(15-15sqrt(5))/2

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x^{3} - 30 x^{2} + 1 5^{3} = 0

x = 15, x = \frac{15 + 15 5}{2}, x = \frac{15 - 15 5}{2}

Decimal Notation

x = 15, x = 24.27050 \dots, x = - 9.27050 \dots

Solution steps

x^{3} - 30 x^{2} + 1 5^{3} = 0

Expand

x^{3} - 30 x^{2} + 1 5^{3} : x^{3} - 30 x^{2} + 3375

x^{3} - 30 x^{2} + 3375 = 0

Factor

x^{3} - 30 x^{2} + 3375 : (x - 15) (x^{2} - 15 x - 225)

(x - 15) (x^{2} - 15 x - 225) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 15 = 0 or x^{2} - 15 x - 225 = 0

Solve

x - 15 = 0 : x = 15

Solve

x^{2} - 15 x - 225 = 0 : x = \frac{15 + 15 5}{2}, x = \frac{15 - 15 5}{2}

The solutions are

x = 15, x = \frac{15 + 15 5}{2}, x = \frac{15 - 15 5}{2}

x^{3} - 7 x^{2} + 6 x + 20 = 0

- 10 x^{4} + 6 = 0

- 4 s^{3} - 24 s^{2} - 72 s - 80 = 0

x^{3} - 7 x^{2} + 17 x + 25 = 0

3 x^{6} - 4 x^{3} - 46375 = 0

What are the solutions to the equation x^3-30x^2+15^3=0 ?
The solutions to the equation x^3-30x^2+15^3=0 are x=15,x=(15+15sqrt(5))/2 ,x=(15-15sqrt(5))/2
Find the zeros of x^3-30x^2+15^3=0
The zeros of x^3-30x^2+15^3=0 are x=15,x=(15+15sqrt(5))/2 ,x=(15-15sqrt(5))/2