What are the solutions to the equation 4(x)^3+x-1=0 ?

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

Find the zeros of 4(x)^3+x-1=0

The zeros of 4(x)^3+x-1=0 are x= 1/2 ,x=-1/4+i(sqrt(7))/4 ,x=-1/4-i(sqrt(7))/4

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4 (x)^{3} + x - 1 = 0

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

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

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

x^{4} + 2 x^{3} - 7 x^{2} - 8 x + 12 = 0

x \cdot (x^{2} - 6) - 1 \cdot (x - 6) = 0

x^{5} - 12 x^{3} + 24 = 0

a^{2} - a^{3} = 100

m^{4} - 2 m^{3} + 7 m^{2} - 5 m = 0

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