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Consider the cubic equation x³+bx²+cx +d = 0.If the roots of the equation are in A.P. then (A) b³= 27d (B) 2b³-9bc+27d =0 (C)27d³=9bcd²-2c³d (D)b³d=c³
Let p,q,r be the roots of eq.Given, they are in A.P 》p+r=2q And also by cubic p+q+r = -b 》3q = -bNow you know that -b/3 is a root of the cubic. So put x= -b/3 to get the relation b/w b,c and d.The answer is option (B)
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