(i)[3]
Determine the values of $a$ and $b$.
(ii)[4]
Show that the equation $q(x) - p(x) = 0$ has just one real root.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
The polynomials $p(x)$ and $q(x)$ are given by $p(x) = x^3 + x^2 + ax - 15$ and $q(x) = 2x^3 + x^2 + bx + 21$, with $a$ and $b$ as constants. It is stated that $(x + 3)$ is a factor of $p(x)$ and also a factor of $q(x)$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Put $x=-3$ into either $p(x)$ or $q(x)$ and set the result equal to zero” …
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