Solve each quadratic equation by completing the square. give exact answers--no decimals.

Step-by-step explanation:

In this problem we have the equation of the following quadratic equation and we want to solve it using the method of square completion:

The steps are shown below:

For any equation of the form:

1. If the coefficient a is different from 1, then take a as a common factor.

In this case . Then we go directly to step 2

2. Take the coefficient b that accompanies the variable x. In this case the coefficient is 6. Then, divide by 2 and the result squared it.

We have:

3. Add the term obtained in the previous step on both sides of equality

4. Factor the resulting expression, and you will get:

Now solve the equation:

Note that the term is always > 0 therefore it can not be equal to -32.

The equation has no solution in real numbers.

In the same way we can find the complex roots:

f(x) = x^3 -2x^2 -3x

x( x^2 -2x-3)

x( x^2 +x -3x -3)

x( x(x+1) -3(x+1))

x( x-3)( x+1)

so zeroes are 0, 3,-1

its (2) option