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ASESMEN SUMATIF 3A

1. Tentukan Penyelesaian Persamaan Kuadrat (Metode Akar Kuadrat): a. $x^2 = 36$ $x = \pm \sqrt{36} = \pm 6$

   b. $9n^2 - 25 = 0$ $9n^2 = 25 \quad \Rightarrow \quad n^2 = \frac{25}{9} \quad \Rightarrow \quad n = \pm \frac{5}{3}$

   c. $(y+2)^2 = 100$ $y + 2 = \pm \sqrt{100} = \pm 10 \quad \Rightarrow \quad y = -2 \pm 10$ $y = 8 \text{ or } y = -12$

2. Tentukan Akar-Akar dari Persamaan Kuadrat (Metode Pemfaktoran): a. $x^2 + 10x = -21 \quad \Rightarrow \quad x^2 + 10x + 21 = 0$ $(x + 3)(x + 7) = 0 \quad \Rightarrow \quad x = -3 \text{ or } x = -7$

   b. $x^2 - 2x - 24 = 0$ $(x - 6)(x + 4) = 0 \quad \Rightarrow \quad x = 6 \text{ or } x = -4$

   c. $2x^2 - 3x + 30 = 0$ (This equation has no real roots since the discriminant is negative.)

3. Dengan Rumus Kuadrat ($ax^2 + bx + c = 0$): a. $y^2 + 3y - 28 = 0$ $y = \frac{-3 \pm \sqrt{3^2 - 4(1)(-28)}}{2(1)} = \frac{-3 \pm \sqrt{121}}{2} = \frac{-3 \pm 11}{2}$ $y = 4 \text{ or } y = -7$

   b. $2x^2 + x - 6 = 0$ $x = \frac{-1 \pm \sqrt{1^2 - 4(2)(-6)}}{2(2)} = \frac{-1 \pm \sqrt{49}}{4} = \frac{-1 \pm 7}{4}$ $x = \frac{3}{2} \text{ or } x = -2$

4. Masalah Persegi Panjang dengan Luas 300 $m^2$:

   • Panjang $p$, Lebar $l = p - 5$
   • Luas: $p(p - 5) = 300$ $p^2 - 5p - 300 = 0$ Using the quadratic formula: $p = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(-300)}}{2(1)} = \frac{5 \pm \sqrt{1225}}{2} = \frac{5 \pm 35}{2}$ $p = 20 \text{ or } p = -15 \quad (\text{discard } p = -15)$ $p = 20, \quad l = 20 - 5 = 15$

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Tip: Always check the discriminant ($b^2 - 4ac$) to see if a quadratic equation has real solutions.