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

The solutions to the equation 2x^3+x^2+1=0 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=0

The zeros of 2x^3+x^2+1=0 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 = 0

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 = 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}

x^{4} + 3 x^{2} - 1 = 0

n^{2} = \frac{n ( n + 1 ) ( 2 n + 1 )}{6}

x^{4} - 34 x^{2} + 255 = 0

4 x^{3} + 2 x - 6 = 0

67 = a^{3}

What are the solutions to the equation 2x^3+x^2+1=0 ?
The solutions to the equation 2x^3+x^2+1=0 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=0
The zeros of 2x^3+x^2+1=0 are x=-1,x= 1/4+i(sqrt(7))/4 ,x= 1/4-i(sqrt(7))/4