Question

If the roots of the equation, $x ^3+ Px ^2+ Qx -19=0$ are each one more than the roots of the equation, $x ^3- Ax { }^2+ Bx - C =0$, where $A , B , C , P \& Q$ are constants then the value of $A + B + C =$

• A. 18
• B. 19
• C. 20
• D. none

Answer 1

Answer: (A)

Let roots of $x ^3- Ax ^2+ Bx - C =0$ are $\alpha, \beta, \gamma$
$\Rightarrow \alpha+\beta+\gamma= A , \Sigma \alpha \beta= B , \alpha \beta \gamma= C$
$\&(\alpha+1)(\beta+1)(\gamma+1)=19 $
$\Rightarrow(\alpha+\beta+\gamma)+(\alpha \beta+\beta \gamma+\gamma \alpha)+\alpha \beta \gamma+1=19$
$A + B + C =18$