x cubed minus two x squared minus thirty-five x equals zero

Answer 1

To solve the equation x^3 - 2x^2 - 35x = 0, we can factor out an x:

x(x^2 - 2x - 35) = 0

Now, we can solve for x by setting each factor equal to zero:

The first factor, x = 0.

For the second factor, we can use the quadratic formula to find the roots:

x = (-(-2) ± sqrt((-2)^2 - 4(1)(-35))) / (2(1))
x = (2 ± sqrt(4 + 140)) / 2
x = (2 ± sqrt(144)) / 2
x = (2 ± 12) / 2

x = (2 + 12) / 2 => x = 14 / 2 => x = 7
x = (2 - 12) / 2 => x = -10 / 2 => x = -5

Therefore, the solutions to the equation x^3 - 2x^2 - 35x = 0 are x = 0, x = 7, and x = -5.