Question

If m is the number of real roots of ke^x = 5 + x + x²/2 , k ∈ R⁺ then the value of (m + 3) is...

Answer 1

Given equation is

ke^x = 5 + x + x²/2 , k ∈ R⁺

⇒ 2ke^x = 10 + 2x + x²

⇒ 2ke^x = (x + 1)² + 9

Clearly, the number of solution is 1

Thus, m = 1

Hence, the value of (m + 4) is 4.