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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

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

Grade:11

1 Answers

Aakash
13 Points
5 years ago
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 = -b
Now 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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