Trik Jitu #11 - Persamaan Kuadrat

$latex Selisih\ dari\ akar-akar\ persamaan\ kuadrat\ ax^2+bx+c=0\\ditentukan\ oleh\ {\color{red}x_{1}-x_{2}=\frac{\sqrt{D}}{a}}.\\\\{\bf{Keterangan:}}\\D\ adalah\ diskriminan,\ {\color{blue}D=b^2-4ac}.$

Contoh:

$latex Akar-akar\ persamaan\ 2x^2-6x-p=0\ adalah\ x_{1}\ dan\ x_{2}.\\Jika\ x_{1}-x_{2}=5\ maka\ nilai\ p^2-2p\ adalah\ ....\\A.\ \ 42\\B.\ \ 46\\C.\ \ 48\\D.\ \ 64\\E.\ \ 72$

Jawaban: C
$latex \begin{array}{rcl}x_{1}-x_{2}&=&{\large\frac{\sqrt{D}}{a}}}\\\\5&=&\frac{\sqrt{D}}{a}}\qquad .........\quad kuadratkan\\\\25&=&\frac{D}{a^2}\\\\25&=&\frac{b^2-4ac}{a^2}\\\\25&=&\frac{(-6)^2-4(2)(-p)}{2^2}\\\\25&=&\frac{36+8p}{4}\\\\25&=&9+2p\\\\2p&=&16\\\\p&=&8\end{array}$

$latex p^2-2p=8^2-2.8=64-16=48$

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