What are the solutions to the equation x^3-x^2-75/8 =0 ?

The solutions to the equation x^3-x^2-75/8 =0 are x= 5/2 ,x=-3/4+i(sqrt(51))/4 ,x=-3/4-i(sqrt(51))/4

Find the zeros of x^3-x^2-75/8 =0

The zeros of x^3-x^2-75/8 =0 are x= 5/2 ,x=-3/4+i(sqrt(51))/4 ,x=-3/4-i(sqrt(51))/4

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x^{3} - x^{2} - \frac{75}{8} = 0

x = \frac{5}{2}, x = - \frac{3}{4} + i \frac{51}{4}, x = - \frac{3}{4} - i \frac{51}{4}

Solution steps

x^{3} - x^{2} - \frac{75}{8} = 0

Multiply both sides by

8

8 x^{3} - 8 x^{2} - 75 = 0

Factor

8 x^{3} - 8 x^{2} - 75 : (2 x - 5) (4 x^{2} + 6 x + 15)

(2 x - 5) (4 x^{2} + 6 x + 15) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 x - 5 = 0 or 4 x^{2} + 6 x + 15 = 0

Solve

2 x - 5 = 0 : x = \frac{5}{2}

Solve

4 x^{2} + 6 x + 15 = 0 : x = - \frac{3}{4} + i \frac{51}{4}, x = - \frac{3}{4} - i \frac{51}{4}

The solutions are

x = \frac{5}{2}, x = - \frac{3}{4} + i \frac{51}{4}, x = - \frac{3}{4} - i \frac{51}{4}

1400 = 1000 \cdot (1 + x)^{3}

2 x^{3} - 5 x^{2} - 5 x - 1 = 0

2 x^{5} - 5 x^{4} + 10 x^{2} - 10 x + 1 = 0

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

x \cdot x \cdot x = 0.5

What are the solutions to the equation x^3-x^2-75/8 =0 ?
The solutions to the equation x^3-x^2-75/8 =0 are x= 5/2 ,x=-3/4+i(sqrt(51))/4 ,x=-3/4-i(sqrt(51))/4
Find the zeros of x^3-x^2-75/8 =0
The zeros of x^3-x^2-75/8 =0 are x= 5/2 ,x=-3/4+i(sqrt(51))/4 ,x=-3/4-i(sqrt(51))/4