The curve $y=(x-2)(x-5)$ intersects the coordinate axes at $A$, $B$ and $C$, as shown. The s

Question

The curve $y=(x-2)(x-5)$ intersects the coordinate axes at $A$, $B$ and $C$, as shown. The shaded regions are denoted by $P$ and $Q$. Find the coordinates of $A$, $B$ and $C$.[2] Find the areas of $P$ and $Q$.[5] Hence find the ratio of the area of $P$ to the area of $Q$.[1]

Accepted Answer

(i) $A=(0,10)$, $B=(2,0)$, $C=(5,0)$ (ii) $P=\dfrac{26}{3}\text{ units}^2$, $Q=\dfrac92\text{ units}^2$ (iii) $52:27$

Unequal regions on opposite sides of the x-axis

Unequal regions on opposite sides of the x-axis

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