Question

Instructions: Select all of the methods that will find both real and imaginary solutions.

Answer 1

Recall that:

1) The quadratic formula states that the solutions to the quadratic equation:

`ax^2+bx+c=0`

are:

`x=(-b\pm√(b^2-4ac))/(2a).`

The above formula gives us the solutions (real or imaginary) to any quadratic equation.

2) The square roots method allows to determine the solutions to the equations of the form:

`x^2+c=0.`

If c>0 we will get imaginary solutions, and if c≤0 we will get real solutions.

3) The Compleating the Square consists of completing the perfect trinomial to be able to factor it, this method gives us both real and imaginary solutions to a quadratic equation.

4) Sometimes we cannot factor a quadratic equation as a product of binomials, therefore this method only gives us real solutions.

Answer:

Quadratic Formula.

Square Roots.

Completing the Square.