If c R be such that the line 4 x-y+c=0 touches the ellipse x^2+4 y^2=4 , then an equation having all such values of c among its roots is

Step-by-step solution

If line 4 x-y+c=0 touches the ellipse x^2 4 + y^2 1 =1 , then aligned & c^2=4(4)+1 c^2=17 & c= 17 aligned Now, from the options, the equation aligned & x^3-x^2-17 x+17=0 & x^2(x-1)-17(x-1)=0 & (x-1) (x^2-17 )=0 & x=1, 17 aligned The cubic equation x^3-x^2-17 x+17=0 have roots 17 . Hence, option (c) is correct.