Question

If one root of $x^{2} +px+1=0$ is square of the other, then p =
1) 1, -2
2) 3, -1
4) 2, -5
4) 2, 3

Answer 1

i did it!!! the answer is 1,-2 but this app is not letting me to post it.

so i will tell you the method
first of all take roots as alpha and alpha square then

write both the equations of sum of roots and product of roots
then cube both the sides of sum of roots equation

then substitute the value of alpha cube and (alpha)(alpha +1) then you'll get a cubic equation with p as a variable solve it and its factors will be 1 and -2