The curve C 1 has equation y = a/x 2 where a is a positive constant. The

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The curve C1 has equation y = −a/x2 where a is a positive constant. The curve C2 has the equation y = x2 (3x + b) where b is a positive constant.

a. Sketch C1 and C2 on the same set of axes, showing clearly the coordinates of any point where the curves touch or cross the axes.

b. Using your sketch state, giving reasons, the number of solutions to the equation x4(3x + b) + a = 0.

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