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

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

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

The zeros of 1-3x^2+2x^3=0 are x=1,x=-1/2

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

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

Decimal Notation

x = 1, x = - 0.5

Solution steps

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

Write in the standard form

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

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or 2 x + 1 = 0

Solve

x - 1 = 0 : x = 1

Solve

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

The solutions are

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

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

5 (x^{2} + x - 12) (x - 8) = 0

k^{4} + 2 k^{3} - 3 k^{2} - 6 k + 1 = 0

x^{4} - (5 + 2) x^{2} + 10 = 0

(x - 3)^{3} = 2 x (x^{2} - 1)

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