Question

Write the condition for the both roots of f(x) =0 to be greater than a given number k.
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Answer 1

Answer:

Let f(x)=4x

2

−20Px+(25P

2

+15P−66) ...(1)

The roots of (1) are real if

b

2

−4ac=400P

2

−16(25P

2

+15P−66)=16(66−15P)≥0

⇒P≤

5

22

...(2)

Both roots of (1) are less than 2.

Therefore, f(2)>0 and sum of roots <4.

⇒4.2

2

−20P.2+(25P

2

+15P−66)>0 and −(−20+15)P<4

⇒P

2

−P−2>0 and P<

5

4

⇒(P+1)(P−2)>0 and P<

5

4

⇒P<−1 and P<

5

4

⇒P<−1 ...(3)

From (2) and (3), we get P<−1⇒P∈(−∞,−1)

Step-by-step explanation:

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