What are the solutions to the equation x^3+2x^2-1=0 ?

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

Find the zeros of x^3+2x^2-1=0

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

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

x = - 1, x = \frac{- 1 + 5}{2}, x = \frac{- 1 - 5}{2}

Decimal Notation

x = - 1, x = 0.61803 \dots, x = - 1.61803 \dots

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 1 = 0 : x = - 1

Solve

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

The solutions are

x = - 1, x = \frac{- 1 + 5}{2}, x = \frac{- 1 - 5}{2}

(x^{2} - 1) \cdot (5 - x) = 0

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

a, a^{4} b + 2 c^{5} = d^{1} e

8 m^{3} - 104 m^{2} + 336 m = 0

5 x^{3} - 29 x + 30 = 0

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