# How do you find the value of the discriminant and state the type of solutions given #8b^2-6n+3=5b^2#?

##### 1 Answer

Assumption: The only variable is

#### Explanation:

Taken as:

Subtract

Compare to

Where

In your case

The discriminant part is the

So the discriminant is 0

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However, if the discriminant is 0 as in this case you have:

giving a single value solution. Consequently the x-axis behave like a tangent to the curve at the min/max point.

So the curve does not actually cross the axis but it more like the two coincide.

However; some people argue that their is always 2 solution but the condition we have hear has the sate of 'duality'.

I am guessing this means that the two solutions happen to coincide thus look as though there is one. This is higher maths 'stuff'.