Let α and β be the roots of $x^2-9x+14=0$. The quadratic equation whose two roots are the number α + β and the number αβ is:

For the given equation α + β = 9 and αβ = 14, so the two new roots are the plain numbers 9 and 14. They add to 23 and multiply to 126, giving $x^2-23x+126=0$. (Carrying the old product 14 forward gives the first option, and interchanging the roles of sum and product gives $x^2-126x+23=0$.) Substituting $x=9$: 81 − 207 + 126 = 0, and $x=14:196-322+126=0$.