Question

Suppose $f\left(x\right)=e^{ax}+e^{bx}$, where $a\ne b$, and that $f"\left(x\right)-2f"\left(x\right)-15f\left(x\right)=0$ for all x. Then the product ab is equal to

• A. 25
• B. 9
• C. -15
• D. -9

Answer 1

The correct option is C

-15

$(a^2-2a-15)e^{ax}+(b^2-2b-15)e^{bx}=0$
$\Rightarrow a^2-2a-15=0$ and $b^2-2b-15=0$
$\Rightarrow a=5$ or $–3$ and $b=5$ or $–3$
$\therefore a\ne b$ hence $a=5$ and $b=-3$
or $a=-3$ and $b=5$
$\Rightarrow ab=-15$