IAL 2025 May FP1 Q3

Question

[!problem]

(i) $f(x) = x^2 + 5 - 85x$

Given that the equation $f(x) = 0$ has a single root, $\alpha$, in the interval $[0, 1]$

use interval bisection to determine an interval of width 0.25 that contains $\alpha$.

(3)

(ii) $g(x) = 3\sin x - 3\cos x$

where $x$ is in radians.

(a) Show that the equation $g(x) = 0$ has a root, $\beta$, in the interval $[4, 5]$

(2)

(b) Use linear interpolation once on the interval $[4, 5]$ to determine an approximation for $\beta$.

Give your answer to 4 significant figures.

(2)