# How do you know if a quadratic equation can be factored?

The answer depends on what the factors will be. For example, every quadratic can be factored if you allow complex numbers.

If not, then it helps to use the discriminant.

If it is positive, there are two real factors or solutions.

If that positive number is a perfect square, then the factors are rational numbers.

If not, they are real but not rational (irrational).

If the discriminant is 0, there is one real solution.

Lastly, if it is negative, there are no real solutions.

### Which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring?

Here are two ways to know if a given quadratic equations can be factored (can be solved by factoring). 1. Calculate the Discriminant D = b^2 - 4ac. When D is a perfect square (its square root is a whole number), then the given equation can be factored. 2. Solve the equation by using the new Diagonal Sum method (Amazon e-book 2010). This method directly finds the 2 real roots without having to factor the…

### What are the steps to solving a quadratic equation?

In general, there are two steps in solving a given quadratic equation in standard form ax^2 + bx + c = 0. If a = 1, the process is much simpler. The first step is making sure that the equation can be factored? How? In general, it is hard to know in advance if a quadratic equation is factorable. I suggest that you use first the new Diagonal Sum Method to solve the equation. It…

### What are two algebraic methods for solving quadratic equations?

Finally, there are two methods to use, depending on if the given quadratic equation can be factored or not. 1.- The first one is the new Diagonal Sum Method, recently presented in book titled: "New methods for solving quadratic equations" (Trafford 2009). This method directly gives the two roots in the form of two fractions, without having to factor it. The innovative concept of this new method is finding 2 fractions knowing their product (c/a)…

### What are the 4 methods to solve a quadratic equation?

You can solve a quadratic equation 4 different ways. graphing, which is quick but not reliable, factoring, completing the square and using the quadratic formula. There is a new fifth method, called Diagonal Sum Method, that can quickly and directly give the 2 roots in the form of 2 fractions, without having to factor the equation. It is fast, convenient, and is applicable whenever the equation can be factored. Finally, you can proceed solving in…

### How do you solve quadratic equations by factoring?

There is a new method, called Diagonal Sum Method, that quickly and directly give the 2 roots without having to factor the equation. The innovative concept of this method is finding 2 fractions knowing their sum (-b/a) and their product (c/a). It is fast, convenient and is applicable to any quadratic equation in standard form ax^2 + bx + c = 0, whenever it can be factored. If it fails to find answer, then the…

### How many existing methods are there in solving quadratic equations?

There are 5 existing methods in solving quadratic equations. For the first 4 methods (quadratic formula, factoring, graphing, completing the square) you can easily find them in algebra books. I would like to explain here the new one, the Diagonal Sum Method, recently presented in book titled:"New methods for solving quadratic equations and inequalities" (Trafford 2009). It directly gives the 2 roots in the form of 2 fractions, without having to factor the equation. The…