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:#" "8b^2-6b+3=5b^2#

Subtract #5b^2# from both sides

#3b^2-6b+3=0#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

To avoid confusion let #b=t#

Then we have: #3t^2-6t+3#

Compare to #y=at^2+bt+c=0#

#a=3"; "b=-6"; "c=3#

Where #t=(-b+-sqrt(b^2-4ac))/(2a)#

#=>t=(+6+-sqrt(6^2-4(3)(3)))/(2(3))#

The discriminant is:

#b^2-4ac ->36 - 36 = 0#

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.

Tony B