Question

If $a{x}^2+bx+c=0andb{x}^2+cx+a=0$ have a common root and a,b,c are non - zero real numbers then$\frac{a^3+b^3+c^3}{abc}$ is equal to :

• A. 1
• B. 2
• C. 3
• D. None

Answer 1

The correct option is C

3

$a{x}^2+bx+c=0andb{x}^2+cx+a=0$ has a common root, then

$\frac{x^2}{ab-c^2}=\frac{x}{cb-a^2}=\frac{1}{ac-b^2}$

$\Rightarrow$ $(cb-a^2{)}^2=(ab-c^2\left)\right(ac-b^2)$

$\Rightarrow$ $a^3+b^3+c^3=3abc$