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# Given,for three distinct real numbers a,b,c $\in R,a(a^2+p)=b(b^2+p)=c(c^2+p)$.The value of $a+b+c$ is

$\begin{array}{1 1}(A)\;0&(B)\;1\\(C)\;3&(D)\;\text{None}\end{array}$

Let $a(a^2+p)=b(b^2+p)=c(c^2+p)=k$
Then $x(x^2+p)=k$ has a,b,c as roots
$\Rightarrow x^3+px-k=0$
$a+b+c$=sum of roots=zero
Hence (A) is the correct answer.

+1 vote