# How do you find the discriminant of #7x^2+6x+2=0# and use it to determine if the equation has one, two real or two imaginary roots?

##### 2 Answers

#### Explanation:

Consider the standard format of

Where

The discriminant is the part of

If this is 0 then the vertex is actually on the on the axis so has 1 point

If this is negative then the roots are complex numbers

If this is positive and greater than 0 then it has two roots

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Added comment: I have had people argue that when the discriminant is 0 there is still 2 roots but they are the same value. This condition is called duplicity.

I do not like this!

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So for this equation:

Discriminant

So

The solutions are

#### Explanation:

The quadratic equation is

Here, we have

The discriminant is

As

The roots are imaginary