Question

If alpha and beta are the zeroes of the polynomial 6x²+x-2 then find alpha ⁴+beta⁴

Answer 1

Answer:

since, à and ß are the zeroes of the given polynomial

so, à+ß= -b/a= -1/6

à.ß=c/a =-2/6=-1/3

Now, à⁴+ß⁴=[(à+ß)²-2àß]²-2à²ß²

=[(-1/6)²-2×(-1/3)]²-2(-1/3)²

=[1/36+2×1/9]²-2×1/9

=[1+8/36]²-2/9

=(9/36)²-2/9

=(1/4)²-2/9

=1/16-2/9

=9-32/144

=-23/144