Suppose `f(x)=e^(ax) + e^(bx)`, where `a!=b`, and that `fprimeprime(x)-2fprime(x)-15f(x)=0` for all `x`. Then the value of `ab` is equal to:

Options

A. 25
B. 9
C. -15
D. -9

Explanation

`(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`