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

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

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

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

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

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

Decimal Notation

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

Solution steps

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

Write in the standard form

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

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}

19.6 y^{3} - 40.57 y^{2} + 25 = 0

(8 x^{7}) + (8 x^{4}) = 8 x (x)

x^{4} + i x = i x - i + 3

x^{4} + 6 \cdot x^{2} - 60 x + 36 = 0

x^{4} - 6 x^{2} = 27

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