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

1 Answer
Jan 31, 2017

Answer:

Assumption: The only variable is #n#

Explanation:

#color(blue)("Determine the discriminant")#

Taken as: #8n^2-6n+3=5n^2#

Subtract # 5n^2# from both sides

#color(red)(3n^2-6n+3=0) larr" Use this one"#

Compare to #y=ax^2+bx+c = 0#

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

In your case #x# is #n#

The discriminant part is the #b^2-4ac# giving

#(-6)^2-4(3)(3) = 36-36=0#

So the discriminant is 0
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#color(blue)("Further comments")#

#color(red)("IF")# the graph crosses the x-axis in two different places the quadratic formula results in a solution of format:

#"some value " +-" some other value"#

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

#"some value " +-" "0#

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'.