Find the sum of the y coordinates of the four points of intersection of y = x4 – 5x2 – x + 4 and y = x2 – 3x.
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Solving simultaneously the two equations
we have, x4 – 5x2 – x + 4 = x2 – 3x
x4 – 6x2 + 2x + 4 = 0 .....(1)
let a, b, c and d be the root of (1)
a + b + c + d = 0 and
now y1 = a2 – 3a, y2 = b2 – 3b and so on
= 0 – 2(– 6) = 12
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