Quadratic equation from given zeros

Let the required quadratic equation be ax2+ bx + c = 0 (a ≠ 0)
when roots of this equation are α and β are given.
Therefore, the empirical relationship between α and β are :

 α + β = - ba

and αβ = ca

Now, ax2+ bx + c = 0

⇒ x2+ bax + ca= 0 (provided, a ≠ 0)