The correct option is D cx2+(b−2c)x+(a−b+c)=0
Given: α,β are the roots of the equation ax2+bx+c=0
To find: Equation with roots 1+1α,1+1β
Let y=1+1x
⇒x=1y−1
Substituting x=1y−1 in ax2+bx+c=0, we get:
a(1y−1)2+b(1y−1)+c=0
⇒a+b(y−1)+c(y−1)2=0
⇒a+by−b+cy2−2cy+c=0
⇒cy2+(b−2c)y+(a−b+c)=0
Now, In terms of x, we get the equation as:
cx2+(b−2c)x+(a−b+c)=0 which is required equation.