Persamaan kuadrat Pakai Rumus ABC :) .... Question from @fikrifadilaah17

fikrifadilaah17 @fikrifadilaah17

September 2022 1 4 Report

Persamaan kuadrat Pakai Rumus ABC :)

DETECTlVE

PEMBAHASAN

Rumus ABC

$\boxed{ \sf x_{1,2} = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} }$

Persamaan kuadrat dengan rumus ABC

1. x² - 6x - 7 = 0

2. 3x² + 7x - 20 = 0

Penyelesaian:

Nomor 1 : x² - 6x - 7 = 0

a = 1
b = -6
c = -7

$\begin{aligned}\sf x_{1,2} &= \sf \frac{ - b \pm \sqrt{ { {b}^{2} - 4ac}} }{2a}\\ \sf &=\sf \frac{ - ( - 6) \pm \sqrt{ {( - 6)}^{2} - 4(1) ( - 7) } }{2(1)} \\ \sf &= \sf \frac{6\pm \sqrt{36 + 28} }{2} \\ \sf &=\sf \frac{6 \pm \sqrt{64} }{2}\\ \sf &=\sf \frac{6 \pm 8 }{2} \end{aligned}$

$\boxed{\begin{aligned}\sf x_{1}&=\sf \frac{6 - 8}{2} = \frac{ - 2}{2} = - 1\\ \sf x_{2}&=\sf \frac{6 + 8}{2} = \frac{14}{2} = 7 \end{aligned}}$

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Nomor 2 : 3x² + 7x - 20 = 0

a = 3
b = 7
c = -20

$\begin{aligned}\sf x_{1,2} &= \sf \frac{ - b \pm \sqrt{ { {b}^{2} - 4ac}} }{2a}\\ \sf &=\sf \frac{ -7 \pm \sqrt{ {7}^{2} - 4(3) ( - 20) } }{2(3)} \\ \sf &= \sf \frac{ - 7\pm \sqrt{49 + 240} }{6} \\ \sf &=\sf \frac{ - 7 \pm \sqrt{289} }{6}\\ \sf &=\sf \frac{ - 7 \pm 17 }{6} \end{aligned}$

$\boxed{\begin{aligned}\sf x_{1}&=\sf \frac{ - 7 - 17}{6} = \frac{ - 24}{6} = - 4\\ \sf x_{2}&=\sf \frac{ - 7 + 17}{6} = \frac{10}{6} = \frac{5}{3} \end{aligned}}$