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Let p and q be real numbers such that th...

Let p and q be real numbers such that the function `f(x)={{:(p^(2)+qx","xge1),(-5px^(2)-6","xlt1):}` is derivable for all `x in R`. Then sum of all possible values of p is

A

4

B

3

C

5

D

6

Text Solution

Verified by Experts

The correct Answer is:
C
`becausef(1)=f(1^(+))=f(1^(-))`
`p^(2)q=p^(2)+q=-5p-6impliesp^(2)+5p+q+6=0` …(1)
`becausef'(1^(+))=f'(1^(-))`
`impliesq=-10p` . . .(2) put in (1) we get `p=2` or `p=3`
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