The equations $x^2 + x + a = 0$ and $x^2 + ax+ 1 = 0$
a) Cannot have a common real root for any value of a b) have common real root for exactly one value of a c) have a common real root for exactly two values of a d) have a common real root for all three values of a
My attempt : I used to quadratic formula to find the roots of the first two equations and then equated any two of them , which after simplification lead me to solve a cube equation in a. Since only one of the roots of the given cubic equation gave a real value of x as an answer , the correct option was b)
I would, however, like to know if there is a more shorter/neater way of doing the same question .