Question
The value of p for which both the roots of the quadratic equation, 
are less than 2 lies in :
Hint:
Here we have given a quadratic equation, we have to find the value of p, where it lies. Find first D and relate inequality with p. Here roots are less than 2 and also find here inequality of p. Here f(2) > 0 so find p here and compare with those and look where it lies
The correct answer is:
Here, we have to find the value of p and where it lies.
Firstly, we have quadratic equation, .
Also, the value of both roots is less than 2.
=0
Now for discriminant,
Solve this,
Now, we know that the root of the value is always less than 2 so we can write,
So, at x = 2 the quadratic equation is positive, we can write,
f(2)>0
solving this by factorization, we have
(p−2) (p+1) >0
p > 2 and p < - 1
Hence,
p∈ (−∞, −1) ∪ (2, ∞) ---(3)
From (1), (2) and (3), we get
p belongs to (- −∞, −1)
Therefore, the correct answer is (- −∞, −1)
In this question, we have to find where the p lies. Here, we use discriminant, which is 
. if D > 0 and D = 0 then real solution but if D < 0 then imaginary solution. Here we also us Factorization of quadratic equations.
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