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

 1) Methods:

-  Quadratic formula.

- Factorization.

- Completing the square.

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

Step-by-step explanation:

 Methods:

-  Quadratic formula

Given the quadratic equation in Standard form , you can solve it with the quadratic formula:

- Factorization

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

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

When you make the multiplication indicated in , you obtain

- Completing the square

Given the quadratic equation in Standard form ,, you must turn it into:

Where:

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:

If then there are two roots that are complex conjugates.

4

step-by-step explanation:

6 (donuts) divided by 3 is 2.

so 2/3 means 2 times 2, which is 4/6.

you get two and your friend gets four.

answer:   35 % is the probability of a late departure or an early arrival.

step-by-step explanation:

let l represents the late departure and e represents the early departure.

then, according to the question,

p(l) = 12 %,   p(e) = 27 % and = 4 %

and, we have to find out,

but, we know that,

which is the required equation that will use to find the probability of a late departure or an early departure.

therefore,   the probability of a late departure or an early arrival =   35 %