Question

If $a^2(a+p)=b^2(b+p)=c^2(c+p)$, then

• A. $a+b+c=0$
• B. $a+b+c=-p$
• C. $ab+bc+ca=p$
• D. $ab+bc+ca=0$

Answer 1

Answer: (B), (D)

The correct options are
B $a+b+c=-p$
D $ab+bc+ca=0$

Let $a^2(a+p)=b^2(b+p)=c^2(c+p)=k$.
Then, $a^3+a^{2}p-k=0,b^3+b^{2}p-k-0,c^3+c^{2}p-k=0$.
Hence, $a,b,c$ are roots of equation $x^3+p{x}^2-k=0$,
where,
$a+b+c=-p$
$ab+bc+ca=0$