# What is the discriminant of #4x^2-4x+11=0# and what does that mean?

##### 1 Answer

#### Explanation:

For a general form quadratic equation

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

the *discriminant* is defined as

#color(blue)(Delta = b^2 - 4ac)#

In your case, you have

which means that

The discriminat will be equal to

The fact that the discriminat is **negative** tells you that this quadratic has **no real solutions**, but that it does have *two distinct imaginary roots*.

Moreover, the graph of the function will have **no**

graph{4x^2 - 4x + 11 [-23.75, 27.55, 3.02, 28.68]}

The two roots will take the form

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

In your case, you have

These roots will be complex numbers