Mathematics 9709 · AS & A Level · Coordinate geometry

Coordinate geometry — practice question

The diagram displays the curve $y = 2x^5 + 3x^3$ together with the line $y = 2x$, and these meet at points $A$, $O$ and $B$.
(i)[2]

Show that the $x$-coordinates of $A$ and $B$ satisfy $2x^4 + 3x^2 - 2 = 0$.

(ii)[3]

Solve $2x^4 + 3x^2 - 2 = 0$ and hence determine the coordinates of $A$ and $B$, giving exact answers.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Set up $2x^5+3x^2=2x$ and rewrite it as $2x^5+3x^2-2x=0$” …

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