Question

Q... TWO DISTINCT POLYNOMIALS f(x) and g(x) are defined as follows;

f(x) = x²+ax+2 g(x) = x²+2x+a

IN THE EQUATION f(x)=0 and g(x) = 0 have a common root then sum of the roots of the equation f(x)+g(x) =0 is ?

Answer 1

on equating the equations, we get,
x2 + ax + 2= x2 + 2x +2
x2 gets cancelled, so we are left with,
(a-2)x=-1(a-2)
which gives us x=-1,
use x=-1 in any of the equations,
like i use, x2 + ax + 2
this gives us a=3,

now adding both the equations, we get,
2x​2+(2+a)x +(2+a)=0
now, sum of roots is -b/a
so, sum of roots is,
= (-2+a)/2
= (-2+3)/2
= 1/2