The equation of smallest degree with real coefficients having 2+3i  as one of its roots is

Let the equation is x2− (sum of the roots) x + product of the roots = 0 One root is 2+3i By the given condition, here coefficients are realTherefore another root is 2−3i Sum of the roots  =  (2+3i)+(2−3i)=4 And  product of the roots =  (2+3i)(2−3i)=13. ∴ the required equation is x2−4x+13=0