$$ \begin{array}{ll} ext { (3) } x^{2}-3 x-2=0 ext { (wortelvorm) } & ext { (4) }-x^{2}-x=-5 ext { (wortelvorm) } \ ext { (5) }-x^{2}-5 x=2 ext { (wortelvorm) } & ext { (6) } \ x^{2}-11 x=-30 \ ext { (7) } x^{2}-12=0 ext { (wortelvorm) } & ext { (8) } \ ext { (9) } & -2 x^{2}+6 x=0 \ ext { (9) } 4 x^{2}-4 x-3=0 & ext { (10) } 3 x^{2}+8 x=-2 ext { (twee desima }\end{array} $$

Question

$$ \begin{array}{ll}	ext { (3) } x^{2}-3 x-2=0 	ext { (wortelvorm) } & 	ext { (4) }-x^{2}-x=-5 	ext { (wortelvorm) } \ 	ext { (5) }-x^{2}-5 x=2 	ext { (wortelvorm) } & 	ext { (6) } \ x^{2}-11 x=-30 \ 	ext { (7) } x^{2}-12=0 	ext { (wortelvorm) } & 	ext { (8) } \ 	ext { (9) } & -2 x^{2}+6 x=0 \ 	ext { (9) } 4 x^{2}-4 x-3=0 & 	ext { (10) } 3 x^{2}+8 x=-2 	ext { (twee desima }\end{array} $$

UpStudy AI · Accepted Answer

Natuurlijk, laten we de kwadratische vergelijkingen omzetten naar **wortelvorm** en de oplossingen berekenen. Hierbij geef ik zowel de exacte oplossingen als de benaderde waarden tot op twee decimalen.

---

### (3) $$ x^{2} - 3x - 2 = 0 $$

**Wortelvorm:**
$$
x = \frac{3 \pm \sqrt{9 + 8}}{2} = \frac{3 \pm \sqrt{17}}{2}
$$

**Oplossingen:**
$$
x_1 = \frac{3 + \sqrt{17}}{2} \approx 3.56
$$
$$
x_2 = \frac{3 - \sqrt{17}}{2} \approx -0.56
$$

---

### (4) $$ -x^{2} - x = -5 $$

**Stappen:**
$$
-x^{2} - x + 5 = 0 \quad \Rightarrow \quad x^{2} + x - 5 = 0
$$

**Wortelvorm:**
$$
x = \frac{-1 \pm \sqrt{1 + 20}}{2} = \frac{-1 \pm \sqrt{21}}{2}
$$

**Oplossingen:**
$$
x_1 = \frac{-1 + \sqrt{21}}{2} \approx 1.79
$$
$$
x_2 = \frac{-1 - \sqrt{21}}{2} \approx -2.79
$$

---

### (5) $$ -x^{2} - 5x = 2 $$

**Stappen:**
$$
-x^{2} - 5x - 2 = 0 \quad \Rightarrow \quad x^{2} + 5x + 2 = 0
$$

**Wortelvorm:**
$$
x = \frac{-5 \pm \sqrt{25 - 8}}{2} = \frac{-5 \pm \sqrt{17}}{2}
$$

**Oplossingen:**
$$
x_1 = \frac{-5 + \sqrt{17}}{2} \approx -0.44
$$
$$
x_2 = \frac{-5 - \sqrt{17}}{2} \approx -4.56
$$

---

### (6)
*Er lijkt geen vergelijking te zijn opgegeven voor nummer 6.*

---

### (7) $$ x^{2} - 11x = -30 $$

**Stappen:**
$$
x^{2} - 11x + 30 = 0
$$

**Wortelvorm:**
$$
x = \frac{11 \pm \sqrt{121 - 120}}{2} = \frac{11 \pm 1}{2}
$$

**Oplossingen:**
$$
x_1 = \frac{12}{2} = 6
$$
$$
x_2 = \frac{10}{2} = 5
$$

---

### (8) $$ x^{2} - 12 = 0 $$

**Wortelvorm:**
$$
x = \pm \sqrt{12} = \pm 2\sqrt{3}
$$

**Oplossingen:**
$$
x_1 = 2\sqrt{3} \approx 3.46
$$
$$
x_2 = -2\sqrt{3} \approx -3.46
$$

---

### (9) $$ -2x^{2} + 6x = 0 $$

**Stappen:**
$$
-2x^{2} + 6x = 0 \quad \Rightarrow \quad -2x(x - 3) = 0
$$

**Oplossingen:**
$$
x = 0 \quad \text{of} \quad x = 3
$$

---

### (9) $$ 4x^{2} - 4x - 3 = 0 $$

**Wortelvorm:**
$$
x = \frac{4 \pm \sqrt{16 + 48}}{8} = \frac{4 \pm \sqrt{64}}{8} = \frac{4 \pm 8}{8}
$$

**Oplossingen:**
$$
x_1 = \frac{12}{8} = 1.5
$$
$$
x_2 = \frac{-4}{8} = -0.5
$$

---

### (10) $$ 3x^{2} + 8x = -2 $$

**Stappen:**
$$
3x^{2} + 8x + 2 = 0
$$

**Wortelvorm:**
$$
x = \frac{-8 \pm \sqrt{64 - 24}}{6} = \frac{-8 \pm \sqrt{40}}{6} = \frac{-8 \pm 2\sqrt{10}}{6} = \frac{-4 \pm \sqrt{10}}{3}
$$

**Oplossingen:**
$$
x_1 = \frac{-4 + \sqrt{10}}{3} \approx -0.28
$$
$$
x_2 = \frac{-4 - \sqrt{10}}{3} \approx -2.39
$$

---

Mocht je verdere verduidelijking nodig hebben of andere vragen hebben, laat het gerust weten!
Here are the solutions to the quadratic equations in the given list: 1. **(3) $$ x^{2} - 3x - 2 = 0 $$** - Solutions: $$ x \approx 3.56 $$ and $$ x \approx -0.56 $$ 2. **(4) $$ -x^{2} - x = -5 $$** - Solutions: $$ x \approx 1.79 $$ and $$ x \approx -2.79 $$ 3. **(5) $$ -x^{2} - 5x = 2 $$** - Solutions: $$ x \approx -0.44 $$ and $$ x \approx -4.56 $$ 4. **(6)** - No equation provided. 5. **(7) $$ x^{2} - 11x = -30 $$** - Solutions: $$ x = 6 $$ and $$ x = 5 $$ 6. **(8) $$ x^{2} - 12 = 0 $$** - Solutions: $$ x \approx 3.46 $$ and $$ x \approx -3.46 $$ 7. **(9) $$ -2x^{2} + 6x = 0 $$** - Solutions: $$ x = 0 $$ and $$ x = 3 $$ 8. **(9) $$ 4x^{2} - 4x - 3 = 0 $$** - Solutions: $$ x \approx 1.5 $$ and $$ x \approx -0.5 $$ 9. **(10) $$ 3x^{2} + 8x = -2 $$** - Solutions: $$ x \approx -0.28 $$ and $$ x \approx -2.39 $$ If you need further explanations or assistance with any of these solutions, feel free to ask!

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Algebra Questions