show that the equation 3x +2cosx + 5 = 0 has exactly one real root? incorporate the intermediate value theorem and rolles theorem.
Let $\displaystyle f(x) = 3x + 2 cos x + 5$.
Use IVT to show there's at least one root.
Now assume two roots x = a and x = b, that is f(a) = f(b) = 0. Apply Rolles Theorem over the interval [a, b] and show that you get a false conclusion for real numbers.