https://file.aiquickdraw.com/mathbot/file/17274264126649trfxnnv.jpg

I see an image of a mathematical problem projected onto a screen. The problems are as follows:

### a) \( a^2 - 5a - 6 = \)
This is a quadratic equation, which we can factor or solve using the quadratic formula.

### b) \( b^4 - 16 = \)
This is a difference of squares equation, which can be factored as well.

Let’s solve each one:

### Part (a) \( a^2 - 5a - 6 = 0 \)
To factor this:
1. We need two numbers that multiply to \(-6\) and add to \(-5\).
   - The numbers are \(-6\) and \(1\).
2. So we can factor it as: 
   \[
   (a - 6)(a + 1) = 0
   \]
   Solving for \(a\), we get:
   \[
   a = 6 \quad \text{or} \quad a = -1
   \]

### Part (b) \( b^4 - 16 = 0 \)
This is a difference of squares, which can be factored as:
\[
b^4 - 16 = (b^2 - 4)(b^2 + 4) = 0
\]
Now, solve each part:
- \( b^2 - 4 = 0 \) gives \( b^2 = 4 \), so \( b = 2 \) or \( b = -2 \).
- \( b^2 + 4 = 0 \) has no real solutions because \( b^2 = -4 \) has no real roots (but if we consider complex solutions, \( b = 2i \) and \( b = -2i \)).

### Final answers:
- For part (a): \( a = 6 \) or \( a = -1 \)
- For part (b): \( b = 2 \) or \( b = -2 \), and the complex roots \( b = 2i \), \( b = -2i \).

Would you like any more details or explanations?

### Relative Questions:
1. How do you factor a quadratic equation in general?
2. Can you explain how the difference of squares formula works?
3. What is the quadratic formula, and how can it be applied to part (a)?
4. What are complex numbers, and how do they relate to the solutions in part (b)?
5. How can we graphically interpret the roots of quadratic and quartic equations?

### Tip:
When dealing with quadratic equations, always check if the equation can be factored before using the quadratic formula—it often simplifies the process!

Learn how to solve the quadratic equation a^2 - 5a - 6 and the difference of squares b^4 - 16. This guide provides detailed steps, covering key algebraic concepts like factoring and solving equations. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation