Question

The equation e^x–8 + 2x – 17 = 0 has-

• A. Two real roots
• B. One real root
• C. Eight real roots
• D. Four real roots

Answer 1

Answer: (B)

One real root

Answer 2

Clearly x = 8 satisfies the given equation. Assume that

ƒ(x) = e^{x – 8} + 2x – 17 = 0 has a real root α other than x = 8. We may suppose that α > 8 (the case for α < 8 is exactly similar). Applying Rolle’s theorem on [8, α], we get β ∈

(8, α), such that ƒ′(β) = 0. But ƒ′(β) = e^{β – 8} + 2, So that

e^{β – 8} = –2 which is not possible. Hence there is no real root other than 8.