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
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.
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