Question

If $a^2(a+p)=b^2(b+p)=c^2(c+p),$ where $a,b,c,p\in R,$ then value of $ab+bc+ca$ is

• A. $-p$
• B. $k$
• C. $0$
• D. $p$

Answer 1

The correct option is C $0$

Let $a^2(a+p)=b^2(b+p)=c^2(c+p)=k$
$a^3+p{a}^2-k=0b^3+p{b}^2-k=0c^3+p{c}^2-k=0$

So, $x^3+p{x}^2-k=0$ has roots as $a,b,c.$
Then, $ab+bc+ca=\frac{\text{coefficient of}x}{\text{coefficient of}{x}^3}$
$\therefore ab+bc+ca=0$