https://file.aiquickdraw.com/mathbot/file/1727082562200cscdlecw.jpg

The problem in the image asks to solve quadratic equations using the quadratic formula and round answers to 3 significant figures. Let's start with the selected equations marked in the image: **a**, **e**, and **g**.

### Quadratic Formula:
For a quadratic equation of the form \( ax^2 + bx + c = 0 \), the quadratic formula is:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Now, I'll solve the equations:

#### Equation **(a)**:
\[
x^2 + 6x - 1 = 0
\]
Here, \( a = 1 \), \( b = 6 \), and \( c = -1 \).

#### Equation **(e)**:
\[
x^2 - 3x - 1 = 0
\]
Here, \( a = 1 \), \( b = -3 \), and \( c = -1 \).

#### Equation **(g)**:
\[
x^2 - 8x + 6 = 0
\]
Here, \( a = 1 \), \( b = -8 \), and \( c = 6 \).

I'll now solve these three quadratic equations using the quadratic formula and round the answers to three significant figures.Here are the solutions to the quadratic equations, rounded to three significant figures:

- **Equation (a):** \( x^2 + 6x - 1 = 0 \)
  - Solutions: \( x = 0.162 \), \( x = -6.162 \)

- **Equation (e):** \( x^2 - 3x - 1 = 0 \)
  - Solutions: \( x = 3.303 \), \( x = -0.303 \)

- **Equation (g):** \( x^2 - 8x + 6 = 0 \)
  - Solutions: \( x = 7.162 \), \( x = 0.838 \)

Let me know if you'd like further details or have any questions!

### Related questions:
1. How do you derive the quadratic formula?
2. Why is the discriminant important in solving quadratic equations?
3. Can quadratic equations have complex roots?
4. How does completing the square relate to the quadratic formula?
5. What are some real-world applications of solving quadratic equations?

**Tip:** Always check the discriminant (\(b^2 - 4ac\)) to determine if the roots are real or complex before applying the quadratic formula.

Solve the quadratic equations x^2 + 6x - 1 = 0, x^2 - 3x - 1 = 0, and x^2 - 8x + 6 = 0 using the quadratic formula, and round your answers to 3 significant figures.

Learn how to solve the quadratic equations x^2 + 6x - 1 = 0, x^2 - 3x - 1 = 0, and x^2 - 8x + 6 = 0 using the quadratic formula. This lesson includes step-by-step solutions with answers rounded to 3 significant figures.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation