Question

If the root difference x2 - nx + 24 = 0 equation equals 5, then the number of the equation roots is

Answer 1

$\displaystyle x_1-x_2=5\\\pm\frac{\sqrt{b^2-4ac}}{a}=5\\\pm\frac{\sqrt{(-n)^2-4(1)(24)}}{1}=5\\\pm\sqrt{n^2-96}=5\\n^2-96=25\\n^2=121\\n=\pm11\\\\x_1+x_2=-\frac{b}{a}\\x_1+x_2=-\frac{-n}{a}\\x_1+x_2=\frac{n}{a}\\x_1+x_2=\frac{\pm11}{1}\\\boxed{\boxed{x_1+x_2=\pm11}}$