Question

The equation $e^{x-8}+2x-17=0$ has:

• A. one real root
• B. two real roots
• C. eight real roots
• D. four real roots

Answer 1

The correct option is A

one real root

Explanation for the correct answer:

Finding the number of roots:

Given the equation is $e^{x-8}+2x-17=0$

Let's consider

$e^{x-8}=-2x+17$

If we apply $x=8$ in the above equation, we get

$\begin{array}{rcl}LHS& =& e^{x-8}\\ & =& e^0=1\\ RHS& =& -2x+17\\ & =& -16+17=1\\ LHS& =& RHS\end{array}$

We see that if $x=8$, then $y=1$.

Therefore, $(8,1)$ satisfies the equation and is the solution of the equation.

So, the equation has only one root.

Hence, the correct answer is option (A).