Question

If roots of the equation $a{x}^3+b{x}^2+cx+d=0$ remain unchanged by increasing each coefficient by one unit, then

• A. a = b = c = d $\ne$ 0
• B. $a\ne 0,b+c=0,d\ne 0$
• C. $a\ne b\ne c\ne d\ne 0$
• D. a = b $\ne$ c = d $\ne$ 0

Answer 1

The correct option is A

a = b = c = d $\ne$ 0

$Therootsofa{x}^3+b{x}^2+cx+d=0and(a+1)x^3+(b+1)x^3+(c+1)x+(d+1)=0$ are same.
$\therefore \frac{a+1}{a}=\frac{b+1}{b}=\frac{c+1}{c}=\frac{d+1}{d}\Rightarrow a=b=c=d\ne 0$