persamaan kuadrat x² + x - 2 = 0, akar-akarnya x1 dan x2 dengan x1 < x2. Nilai 2x1 + 3x2 adalah...
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x² + x - 2 = 0
x² + 2x - x - 2 = 0
x(x + 2) - (x + 2) = 0
(x + 2)(x - 1) = 0
•
x + 2 = 0
x = -2
•
x - 1 = 0
x = 1
[tex]~[/tex]
[tex]\begin{aligned}\rm 2x_{1} + 3x_{2} &= \rm2(-2) + 3(1) \\ &= \rm -4 + 3 \\ &= \rm \boxed{-1} \end{aligned}[/tex]
Penjelasan dengan langkah-langkah:
[tex] {x}^{2} + x - 2 = 0 \\ (x - 1)(x + 2) = 0 \\ x - 1 = 0/x + 2 = 0 \\ x = 1/x = - 2 \\ karena \: x1 < x2 \: maka \\ x1 = - 2 \\ x2 = 1 \\ nilai \: 2x1 + 3x2 \\ = 2( - 2) + 3(1) \\ = - 4 + 3 \\ = - 1[/tex]
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