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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