Justify if completing the square is a good method for solving when the Discriminant is negative. Use any of your three functions as an example and respond in complete sentences.

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Question

Justify if completing the square is a good method for solving when the Discriminant is negative. Use any of your three functions as an example and respond in complete sentences.

Heeeeeeeelp. Fan/medal for help? :)

anonymous · Answer

My functions are:

1.	f(x)=x2+6x+5
g(x)=4x2+8x+2
h(x)=6x2+4x+3

tkhunny · Answer

This actually depends on the nature of the underlying question.  Are we to find ONLY Real Solutions?  If so, completing the square is of no value when the Discriminant is negative.  If we seek all solutions, then completing the square is as good as any method.

anonymous · Answer

That helps. But how does that compare with one of my functions?

tkhunny · Answer

Unfortunately, you did not answer my objection.  Are we interested in Real or ALL solutions?  It may not be in the problem statement.  If it is overlooked, I would assume both and point how the response is different.

What is the discriminant for all three?

anonymous · Answer

its -2

tkhunny · Answer

??  f, g, or h?

anonymous · Answer

It doesn't say. All they want to know is if completing the square is a good method when the discriminant is negative.

f(x) has a discriminant of 4.
g(x) has a discriminant of 32
h(x) has a discriminant of -56

tkhunny · Answer

Okay, so h(x) is the most interesting.  What say you?

anonymous · Answer

Fine by me.

tkhunny · Answer

Fair enough.  It is not the time to express your opinion.  Go!

anonymous · Answer

Well, in this scenario, I would say that completing the square wouldn't be the best option because the two solutions are going to be complex since the discriminant is negative.

tkhunny · Answer

Okay, but if you are REQUIRED to find ALL the solutions (Complex or Real), it might be a reasonable practice?

anonymous · Answer

Maybe. Should we work it out to see? I think it depends on what it is you're trying to find, as you've said.

tkhunny · Answer

Nothing to work out.  Just an opinion.  If you want Real solutions and there are none, Completing the Square is a waste of time.  If you need Complex, then one may as well approach it any way that works.

anonymous · Answer

So in a nutshell:
If the discriminant is negative, completing the square is one of the many ways to find complex solutions. But if you wanted to find real solutions in the function h(x), you couldn't because the discriminant is zero and the solutions are only going to be complex.

ranga · Answer

Replace "discriminant is zero" with "discriminant is negative" in your last reply and that pretty much sums up the answer.