The diagram shows a section of the curve with equation y = x 4 + 3x 2

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The diagram shows a section of the curve with equation y = −x4 + 3x2 + 4. The curve intersects the x-axis at points A and B. The finite region R, which is shown shaded, is bounded by the curve and the x-axis.


image


a. Show that the equation −x4 + 3x2 + 4 = 0 only has two solutions, and hence or otherwise find the coordinates of A and B.


b. Find the area of the region R.

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