# What is the discriminant of #x^2 - 5x = 6# and what does that mean?

##### 2 Answers

#### Explanation:

For a quadratic equation that has the general form

#color(blue)(ax^2 + bx + c = 0)#

the **discriminant** can be calculated by the formula

#color(blue)(Delta = b^2 - 4 * a * c)#

Rearrange your quadratic by adding

In your case, you have

SInce **two disctinct real solutions**. Moreover, because *perfect square*, those two solutions will be *rational numbers*.

The general form of the two solutions is given by the *quadratic formula*

#color(blue)(x_(1,2) = (-b +- sqrt(Delta))/(2a)#

In your case, these two solutions will be

so that

Solve:

#### Explanation:

In this case, (a - b + c = 0), use the shortcut --> 2 real roots--> - 1 and

REMINDER of SHORCUT

When (a + b + c = 0) --> 2 real roots: 1 and

When (a - b + c = 0) --> 2 real roots: - 1 and

Remember this shortcut. It will save you a lot of time and effort.