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

detailed solution

Correct option is B

Let roots of ax2+bx+c=0  are α  and β  then                   α+β=−ba  and αβ=ca                                            ……(i)then roots of 2x2+8x+2=0  are           (α−1)  and (β−1)  then          α−1+β−1=−82=−4 ⇒          α+β=−2⇒−ba=−2      (From (i))∴               b=2a and         (α−1)(β−1)=22 ⇒         αβ−α−β+1=1 ⇒              αβ=α+β ⇒               ca=−ba              (From (i))∴          b=−c