Question

The equation formed by the increasing each root of $a{x}^2+bx+c=0$ by $1$, is $2x^2+8x+2=0$, then

• A. $a+b=0$
• B. $b+c=0$
• C. $b=c$
• D. $a=b$

Answer 1

The correct option is C $b=c$

Equation formed by increasing each root of
$a{x}^2+bx+c=0$ by $1$ is
$a(x-1{)}^2+b(x-1)+c=0$
$a(x^2-2x+1)+bx+c-b=0$
$a{x}^2+(b-2a)x+c-b+a=0$
$c-b+a=a$ .... since $2x^2+8x+2=0$ is given equation
$\Rightarrow c-b=0$

$\Rightarrow c=b$