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Menyelesaikan Soal Persamaan Kuadrat SMA

Soal Persamaan Kuadrat

Persamaan kuadrat ${x^2} + 4px + 4 = 0$ mempunyai akar ${x_1}$ dan ${x_2}$. Jika ${x_1}x_2^2 + x_1^2{x_2} = 32$, maka nilai $p$ adalah …


Penyelesaian

$\begin{array}{l} {x^2} + 4px + 4 = 0\\ maka:\\ a = 1\\ b = 4p\\ c = 4\\ Diperoleh:\\ {x_1} + {x_2} = - \frac{b}{a} = - \frac{{4p}}{1} = - 4p\\ {x_1} \times {x_2} = \frac{c}{a} = \frac{4}{1} = 4\\ \begin{array}{*{20}{c}} {Dari}&{soal}&{diketahui:} \end{array}\\ {x_1}x_2^2 + x_1^2{x_2} = 32\\ \Leftrightarrow {x_1}{x_2}\left( {{x_2} + {x_1}} \right) = 32\\ \Leftrightarrow 4\left( { - 4p} \right) = 32\\ \Leftrightarrow - 16p = 32\\ \Leftrightarrow p = \frac{{32}}{{ - 16}}\\ \Leftrightarrow p = - 2 \end{array}$

Jadi nilai $p$ adalah $-2$.

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nurhamim86
nurhamim86 A Mathematics Teacher who also likes the IT world.

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