Question

Suppose f(x) = e^ax + e^bx, where a ≠ b, and that f"(x) – 2f'(x) – 15f(x) = 0 for all x. Then the product ab is ______.

पर्याय

• 25

• 9

• –15

• –9

Answer 1

Suppose f(x) = e^ax + e^bx, where a ≠ b, and that f"(x) – 2f'(x) – 15f(x) = 0 for all x. Then the product ab is –15.

Explanation:

(a² – 2a – 15)e^ax + (b² – 2b – 15)e^bx = 0

or (a² – 2a – 15) = 0 and b² – 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

∴ a ≠ b.

Hence, a = 5 and b = –3 or a = –3 and b = 5 or ab = –15.