2015/026) Given the 2 polynomials

$x^2 + ax + 1 = 0$
$x^2 + x + a = 0$

Find the value of a for which these have at least one root

solution

if both have a common root it shall satisfy the difference of the 2 polynomials

or ax – x + 1 – a = 0 or (x-1)(a-1) =0
so a = 1 or x = 1 giving a = -2