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Suppose f(x)=e^(a x)+e^(b x),w h e r ea!...

Suppose `f(x)=e^(a x)+e^(b x),w h e r ea!=b ,` and that `f^(primeprime)(x)-2f^(prime)(x)-15f(x)=0` for all `x` . Then the product `a b` is (a)`25` (b) `9` (c) `-15` (d) `-9`

A

25

B

9

C

-15

D

-9

Text Solution

Verified by Experts

`(a^(2)-2a-15)e^(ax)+(b^(2)-2b-15)e^(bx)=0`
`"or "(a^(2)-2a-15)=0 and b^(2)-2b-15=0`
`"or "(a-5)(a+3)=0 and (b-5)(b+3)=0`
`i.e., a=5 or -3 and b=5 or -3`
`therefore" "aneb`
Hence, `a=5 and b=-3 or a =-3 and b=5`
`"or "ab=-15`
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