Mathematics 9709 · AS & A Level · Algebra

Algebra — practice question

You are told that $\dfrac{2 + 3ai}{a + 2i} = \lambda(2 - i)$, with $a$ and $\lambda$ both real constants.

(a)[4]

Show that the result is $3a^2 + 4a - 4 = 0$.

(b)[3]

Hence determine the possible values of $a$ together with the corresponding values of $\lambda$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Multiply through by $a+2i$ and then expand.” …