Find the true set of values of 
for which the equation 
has real roots.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. Let 
. Since the range of 
is 
, the range of 
is 
, which is 
, 2].
Substituting 
into the original equation 
:
Solve for p
Multiply the equation by 
to eliminate the fraction:
Rearrange to isolate 
:
Analyze the range of p
To find the set of values for 
, we need to find the range of the function 
over the interval 
.
At 
At 
Using the derivative 
, we see that for 
. This means the function is strictly decreasing on the interval 
.
Final Answer
The equation has real roots if 
falls within the range of 
for 
.
The true set of values for 
is 
.
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