What are the solutions to the equation x^3-17x-4=0 ?

The solutions to the equation x^3-17x-4=0 are x=-4,x=2+sqrt(5),x=2-sqrt(5)

Find the zeros of x^3-17x-4=0

The zeros of x^3-17x-4=0 are x=-4,x=2+sqrt(5),x=2-sqrt(5)

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x^{3} - 17 x - 4 = 0

x = - 4, x = 2 + 5, x = 2 - 5

Decimal Notation

x = - 4, x = 4.23606 \dots, x = - 0.23606 \dots

Solution steps

x^{3} - 17 x - 4 = 0

Factor

x^{3} - 17 x - 4 : (x + 4) (x^{2} - 4 x - 1)

(x + 4) (x^{2} - 4 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 4 = 0 or x^{2} - 4 x - 1 = 0

Solve

x + 4 = 0 : x = - 4

Solve

x^{2} - 4 x - 1 = 0 : x = 2 + 5, x = 2 - 5

The solutions are

x = - 4, x = 2 + 5, x = 2 - 5

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

2 x^{3} + (- 7) x^{2} + 6 x + 5 = 0

b^{3} = 1331

x^{3} - 3.0909 x + 2.0909

- 4 a^{3} + 12 a^{2} - 12 a + \frac{7}{2}

What are the solutions to the equation x^3-17x-4=0 ?
The solutions to the equation x^3-17x-4=0 are x=-4,x=2+sqrt(5),x=2-sqrt(5)
Find the zeros of x^3-17x-4=0
The zeros of x^3-17x-4=0 are x=-4,x=2+sqrt(5),x=2-sqrt(5)