Question

What are the methods for solving quadratic equations and what indicators predict that a quadratic function will have a complex solution?

Answer 1

Answer:

 1) Methods:

-  Quadratic formula.

- Factorization.

- Completing the square.

2) If the determinant is less than zero ($D$) then there are two roots that are complex conjugates.

Step-by-step explanation:

 Methods:

-  Quadratic formula

Given the quadratic equation in Standard form $ax^2+bx+c=0$, you can solve it with the quadratic formula:

$x=\frac{-b\±\sqrt{b^2-4ac}}{2a}$

- Factorization

You must find two expression that when you multply them, you get the original quadratic equation. For example:

$x^2+6x+8=0$

Find two number whose sum is 6 and whose product is 8. These are 2 and 4. Then:

$(x+2)(x+4)=0$

When you make the multiplication indicated in $(x+2)(x+4)=0$, you obtain $x^2+6x+8=0$

- Completing the square

Given the quadratic equation in Standard form $ax^2+bx+c=0$,, you must turn it into:

$a(x+d)^2+e=0$

Where:

$d=\frac{b}{2a}\\\\e=c-\frac{b^2}{4a}$

Once you get that form, you must solve for x.

You can predict if the quadratic function will have a complex solution with the determinant:

$D=b^2-4ac$

If $D$ then there are two roots that are complex conjugates.