Find the range of values of for which is real for all values of .

What's the meaning of the "is real" here??

Does it mean "is true"?

Thanks for those who help :)

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- Nov 27th 2008, 08:35 AMacc100jtquadratic inequality
Find the range of values of for which is real for all values of .

What's the meaning of the "is real" here??

Does it mean "is true"?

Thanks for those who help :) - Nov 27th 2008, 04:38 PMmr fantastic
- Nov 27th 2008, 06:22 PMMathstud28
Let

Then we must find all values of x such that

Now solving we get and

Now since this is an upward facing parabola we want all the values to the "left" and "right" of the two zeros, so we get

and

Now sub back to get

and

So for this value to be real we need to have that or in other words

And that is your answer. - Nov 27th 2008, 08:43 PMmr fantastic
- Nov 27th 2008, 11:56 PMCaptainBlack
Lets assume you are asked to find those values of such that for all .

Well as we have a parabola opening upwards this means that we seek values of such that:

or

has no real roots.

Using the quadratic formula, we find the roots to be:

and for there to be no real roots requires that or .

Which is again Mr Fantastics solution.

CB