Question

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

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

Answer 1

The correct option is B $b=-c$

Since the equation $2x^2+8x+2=0$ has roots which are 1 less than those of the equation $a{x}^2+bx+c=0$ then if we replace $x$ by $x+1$ in latter we'll get the former.
$\Rightarrow a(x+1{)}^2+b(x+1)+c=0$
$\Rightarrow a{x}^2+(2a+b)x+a+b+c=0$
comparing this equation with that of $2x^2+8x+2=0$
we get option (b) as the correct answer