Trik Jitu #10 - Persamaan Kuadrat

$latex Jika\ persamaan\ kuadrat\ {\color{blue}ax^2+bx+c=0}\ mempunyai\ akar\ {\color{blue}x_{1}}\ dan\ {\color{blue}x_{2}}\ dengan\ {\color{blue}x_{1}:x_{2}=m:n}\\maka\ {\color{red}c=\frac{b^2(m\times n)}{a(m+n)^2}}.$

Contoh:

$latex Persamaan\ x^2-8x+k=0\ mempunyai\ akar-akar\ yang\ berbanding\\sebagai\ 3:1,\ harga\ k\ adalah\ ....\\A.\ \ 10\\B.\ \ 12\\C.\ \ 16\\D.\ \ 8\\E.\ \ -8$

Jawaban: B

$latex \large \begin{array}{rcl}k&=&\frac{(-8)^2(3\times 1)}{1(3+1)^2}\\\\&=&\frac{64\times 3}{4^2}\\\\&=&\frac{64\times 3}{16}\\\\&=&4\times 3\\\\&=&12\end{array}$

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