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

The solutions to the equation 2x^3-x^2=1 are x=1,x=-1/4+i(sqrt(7))/4 ,x=-1/4-i(sqrt(7))/4

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

The zeros of 2x^3-x^2=1 are x=1,x=-1/4+i(sqrt(7))/4 ,x=-1/4-i(sqrt(7))/4

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

x = 1, x = - \frac{1}{4} + i \frac{7}{4}, x = - \frac{1}{4} - i \frac{7}{4}

Solution steps

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

Move

1

to the left side

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

2 x^{2} + x + 1 = 0 : x = - \frac{1}{4} + i \frac{7}{4}, x = - \frac{1}{4} - i \frac{7}{4}

The solutions are

x = 1, x = - \frac{1}{4} + i \frac{7}{4}, x = - \frac{1}{4} - i \frac{7}{4}

2 x^{4} = - 64

x^{2} - x^{4} = \frac{1}{16}

7 x^{3} + 21 x^{2} - 63 x = 0

x^{4} + 3 x^{3} - 2 x^{2} - 12 x - 8 = 0

x^{4} + 9 = 10 x^{2}

What are the solutions to the equation 2x^3-x^2=1 ?
The solutions to the equation 2x^3-x^2=1 are x=1,x=-1/4+i(sqrt(7))/4 ,x=-1/4-i(sqrt(7))/4
Find the zeros of 2x^3-x^2=1
The zeros of 2x^3-x^2=1 are x=1,x=-1/4+i(sqrt(7))/4 ,x=-1/4-i(sqrt(7))/4