(a)[4]
Solve the equation $f(x) = 0$, expressing your answers in the form $x = a + b\sqrt{c}$, where $a$, $b$ and $c$ are integers.
(b)[4]
Given that $f(x) = gh(x)$, work out the values of $m$ and $n$.
Mathematics 9709 · AS & A Level · Quadratics
Quadratics — practice question
The functions $f$, $g$ and $h$ are given by:
$f : x \mapsto x - 4x^{\frac{1}{2}} + 1$ for $x \geq 0$,
$g : x \mapsto mx^2 + n$ for $x \geq -2$, where $m$ and $n$ are constants,
$h : x \mapsto x^{\frac{1}{2}} - 2$ for $x \geq 0$.
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