Trik Jitu #8 - Persamaan Kuadrat

$latex Jumlah\ dari\ kuadrat\ akar-akar\ persamaan\ kuadrat\ ax^2+bx+c=0\\ditentukan\ oleh\ {\color{red}{x_{1}}^2+{x_{2}}^2=\frac{b^2-2ac}{a^2}}.$

Contoh:

$latex Bila\ jumlah\ kuadrat\ akar-akar\ persamaan\ x^2-(2m+4)x+8m=0\\sama\ dengan\ 52\ maka\ salah\ satu\ nilai\ m\ adalah\ ....\\A.\ \ 2\\B.\ \ 3\\C.\ \ 4\\D.\ \ 6\\E.\ \ 9$

Jawaban: B
$latex \begin{array}{rcl}{x_{1}}^2+{x_{2}}^2&=&\frac{b^2-2ac}{a^2}\\\\52&=&\frac{\big(-(2m+4)\big)^2-2(1)(8m)}{1^2}\\\\52&=&\frac{(2m+4)^2-16m}{1}\\\\52&=&(2m+4)^2-16m\\\\(2m+4)^2-16m-52&=&0\\\\4m^2+16m+16-16m-52&=&0\\\\4m^2-36&=&0\\\\4m^2&=&36\\\\m^2&=&9\\\\m&=&3\ atau\ m=-3\end{array}$

-->