If α and β are zeroes of quadratic polynomial f(x)=ax²+bx+c then evaluate
(β/aα+b)+(α/aβ+b)
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a and b are roots of ax2+bx+c=0
a+b= -b/a
a2+b2= (a+b)2 -2ab= b2/a2 - 2 c/a= b2/a2 - 2ac/a2
a4+b4= (a2+b2)2 - 2ab times ab
=( b2/a2 - 2ac/a2)2 -2(c/a)2
=b4/a4 + 4a2c2/a4 -4ab2c/a4 - 2a2c2/a4= b4/a4 +2a2c2/a4 - 4ab2c/a4
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