Question

What is a solution to the equation x^3 - 7x2 + 12x = 0?

Answer 1

To solve for the roots of this equation, we can proceed as follows:

`x^3-7x^2+12x=0\Rightarrow x\cdot(x^2-7x+12)=0`

Then, we have two equations to solve for the roots:

1. x = 0.

2. x^2 -7x + 12 = 0

We already have one of the roots of the equation, x = 0.

For the other equation, we know that we can try to find two numbers that if we multiply them, the result must be 12, and if we sum them the result must be -7. Then:

If we have that these numbers are x = -3, and x = -4, we have:

-3 - 4 = -7

-3 * -4 = 12

Then, the roots are the inverse of these two numbers: x = 3, and x = 4.

Therefore, the solutions for the equation: x^3 - 7x^2 + 12 = 0 are:

x = 0

x = 3

x = 4

We can also use the quadratic formula to obtain the roots of the second equation.