What are the solutions to the equation 8x^3-10x^2-7x-1=0 ?

The solutions to the equation 8x^3-10x^2-7x-1=0 are x=-1/4 ,x=(3+sqrt(17))/4 ,x=(3-sqrt(17))/4

Find the zeros of 8x^3-10x^2-7x-1=0

The zeros of 8x^3-10x^2-7x-1=0 are x=-1/4 ,x=(3+sqrt(17))/4 ,x=(3-sqrt(17))/4

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8 x^{3} - 10 x^{2} - 7 x - 1 = 0

x = - \frac{1}{4}, x = \frac{3 + 17}{4}, x = \frac{3 - 17}{4}

Solution steps

8 x^{3} - 10 x^{2} - 7 x - 1 = 0

Factor

8 x^{3} - 10 x^{2} - 7 x - 1 : (4 x + 1) (2 x^{2} - 3 x - 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

4 x + 1 = 0 : x = - \frac{1}{4}

Solve

2 x^{2} - 3 x - 1 = 0 : x = \frac{3 + 17}{4}, x = \frac{3 - 17}{4}

The solutions are

x = - \frac{1}{4}, x = \frac{3 + 17}{4}, x = \frac{3 - 17}{4}

- (x - 3) (x + 5) x^{2} + x - 8 = x - 3 x

x^{4} = 10000

x^{3} + 300 x = 3000

x^{4} = 1000 x

x^{3} - 4 x = 2 x

What are the solutions to the equation 8x^3-10x^2-7x-1=0 ?
The solutions to the equation 8x^3-10x^2-7x-1=0 are x=-1/4 ,x=(3+sqrt(17))/4 ,x=(3-sqrt(17))/4
Find the zeros of 8x^3-10x^2-7x-1=0
The zeros of 8x^3-10x^2-7x-1=0 are x=-1/4 ,x=(3+sqrt(17))/4 ,x=(3-sqrt(17))/4