Engineering
Mathematics
Inequalities
Question

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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Solution
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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    ab=-6

now    y1 = a2 – 3a,    y2 = b2 – 3b  and  so on

  i=14yi=a2+b2+c2+d2-3(a+b+c+d)zero 

=(a+b+c+d)2-2ab

= 0 – 2(– 6) = 12

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