Change of Sign (Edexcel A-Level Mathematics): Flashcards

Finding roots of an equation where $f(x) = 0$.

Look for $[a, b]$ where $f(a)$ and $f(b)$ have opposite signs.

Decimal search or interval bisection methods.

When function is continuous and root isn't repeated.

$f(x) = x^2 + 7x - 12$ has a root in $[1, 2]$.

Plug $x$ into the function definition and solve for $f(x)$.

A root exists in the continuous interval $[1, 2]$.

Must be within [1.8635, 1.8645].

$f(1.8635) > 0$ and $f(1.8645) < 0$ shows a change of sign.

Plug $x$ into the equation; check if it equals $0$.