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The document you've uploaded contains quadratic equation problems. Here are some solutions based on the problems presented:

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### **Question 1:**
Solve \(3x^2 - 3x - 5 = 0\).

**Solution:**

We use the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a = 3\), \(b = -3\), and \(c = -5\).

1. Discriminant: \(\Delta = b^2 - 4ac = (-3)^2 - 4(3)(-5) = 9 + 60 = 69\).
2. Roots:  
   \[
   x = \frac{-(-3) \pm \sqrt{69}}{2(3)} = \frac{3 \pm \sqrt{69}}{6}
   \]
   So, the exact roots are \(x = \frac{3 + \sqrt{69}}{6}\) and \(x = \frac{3 - \sqrt{69}}{6}\).

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### **Question 2:**
Solve \(3x^2 - 14x + 4 = 0\), giving answers accurate to 2 decimal places.

**Solution:**

Using the quadratic formula with \(a = 3\), \(b = -14\), and \(c = 4\):

1. Discriminant: \(\Delta = (-14)^2 - 4(3)(4) = 196 - 48 = 148\).
2. Roots:  
   \[
   x = \frac{-(-14) \pm \sqrt{148}}{2(3)} = \frac{14 \pm 12.1655}{6}
   \]
   Approximate values:  
   \[
   x_1 \approx \frac{14 + 12.1655}{6} \approx 4.36, \quad x_2 \approx \frac{14 - 12.1655}{6} \approx 0.31
   \]

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Would you like more detailed explanations for any of these, or should I solve additional problems from the document?

Here are some related questions to consider:
1. How do you apply the quadratic formula to solve any equation?
2. What is the significance of the discriminant in quadratic equations?
3. What methods exist to solve quadratic equations besides the quadratic formula?
4. How can we factor quadratic equations when the discriminant is a perfect square?
5. Why are some quadratic solutions left in exact form and others in decimal form?

**Tip:** Always check the discriminant first, as it tells you whether you'll have real, repeated, or complex roots.

Solve the quadratic equations using the quadratic formula.

Learn how to solve quadratic equations such as 3x² - 3x - 5 = 0 and 3x² - 14x + 4 = 0 using the quadratic formula. This page explains how to compute exact solutions and solutions rounded to two decimal places, ideal for students in Grades 9-12.

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