Mathematics 9709 · AS & A Level · Quadratics

Quadratics — practice question

For $x \in \mathbb{R}$, the function $f$ is given by $f: x \mapsto x^2 + ax + b$, with $a$ and $b$ as constants.

(i)[3]

When $a = 6$ and $b = -8$, determine the range of $f$.

(ii)[3]

When $a = 5$, the equation $f(x) = 0$ has roots $k$ and $-2k$, where $k$ is constant. Determine $b$ and $k$.

(iii)[3]

Show that the equation $f(x + a) = a$ has no real roots only when $a^2 < 4(b - a)$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Rewrites the expression as $(x+3)^2-17$” …