The correct option is A a(x+k)2+b(x+k)+c=0
Given: ax2+bx+c=0,a≠0 with roots α,β
To find: Quadratic equation whose roots are α−k and β−k
Let t=x−k
Since, x=α⇒t=α−k
x=β⇒t=β−k
Replacing x→t+k in the equation above, we get:
a(t+k)2+b(t+k)+c=0
Now, In terms of variable x, the equation becomes:
a(x+k)2+b(x+k)+c=0 which is the required equation.