For what value/s of constant 'p' for which the given quadratic have both roots as infinity. $(2p^3-13p^2+27p-18)x^2 + (2p^2-9p+9)x +2p^2-7p+6=0$ Options are :- $1) 3/2 2) 2 3) 3 4) /phi $
Since both roots are infinite then sum of the roots must be infinity. For this quadratic let alpha and beta be the roots then we say that Alpha + beta (sum of roots) = -(2p^2-9p+9)/(2p^3-13p^2+27p-18) For the sum to be infinity 2p^3-13p^2+27p-18 must equal to zero. On solving the equation 2p^3-13p^2+27p-18=0 we get p1 =3/2 p2=2 and p3 =3. For p1 and p3 2p^2-9p+9 become zero. So correct option for this question may be 2 but answer in my book is given as option 3. Why this is so.. plz explain me.