What are the solutions to the equation x^3-4x^2+8=0 ?

The solutions to the equation x^3-4x^2+8=0 are x=2,x=1+sqrt(5),x=1-sqrt(5)

Find the zeros of x^3-4x^2+8=0

The zeros of x^3-4x^2+8=0 are x=2,x=1+sqrt(5),x=1-sqrt(5)

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

x = 2, x = 1 + 5, x = 1 - 5

Decimal Notation

x = 2, x = 3.23606 \dots, x = - 1.23606 \dots

Solution steps

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

Factor

x^{3} - 4 x^{2} + 8 : (x - 2) (x^{2} - 2 x - 4)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

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

The solutions are

x = 2, x = 1 + 5, x = 1 - 5

x^{3} + 5 x^{2} + 2 x + 10 = 0

- x (6 x + 7) (x^{2} - 36) = 0

x^{5} + 125 x^{2} = 0

0 = 4 x^{4} - 17 x^{2} + 4

6 x^{3} = 11 x^{2} + 10 x

What are the solutions to the equation x^3-4x^2+8=0 ?
The solutions to the equation x^3-4x^2+8=0 are x=2,x=1+sqrt(5),x=1-sqrt(5)
Find the zeros of x^3-4x^2+8=0
The zeros of x^3-4x^2+8=0 are x=2,x=1+sqrt(5),x=1-sqrt(5)