# How do you find the value of the discriminant and determine the nature of the roots #8b^2-6b+3=5b^2#?

##### 1 Answer

Sep 19, 2016

#### Answer:

The nature of the 'roots' is that 'they' both have the same value. Some people refer to this as duplicity.

In effect, there is only one root.

#### Explanation:

Given:

Subtract

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

To avoid confusion let

Then we have:

Compare to

Where

The discriminant is:

When the discriminant is 0 it means that the x-axis is tangential to the curve at the maximum/minimum point.

The there is a single value solution.