Find a relation between a,b,c so that two quadratic equations ` ax^(2) + bx + c =0 and 1003x^(2) + 1505x + 2007 =0` have a common root.

Explanation

We observe that the discriminant of the quadratic equation ` 1003x^(2) + 1505x + 2007 =0 " is" (1505)^(2) - 4 xx 1003 xx 2007 lt 0`
` Rightarrow ` Root of the equation are complex.
We know that complex roots of an equation occur in conjugate paris, in this case whenever `alpha` be a common root between given equations, other root automatically becomes common.
Hence, the given, equations have both roots common and consequently ` a/1003 = b/1505 = c/2007 = (a +b)/3010 `
` Rightarrow 2b = a+c`
` Rightarrow a ,b,c " are in " A.P.`
WHich is the required relation.