11) For the following equation, use the discriminant to determine the number and type of solutions. y = 3x² - 8x +2 iscriminant Number & type of solutions:
11) For the following equation, use the discriminant to determine the number and type of solutions. y = 3x² - 8x +2 iscriminant Number & type of solutions:
Chapter6: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 7PS
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can anyone help with this? please
![### Quadratic Equation Discriminant Analysis
#### Problem Statement:
11) For the following equation, use the discriminant to determine the number and type of solutions.
\[ y = 3x^2 - 8x + 2 \]
#### Formula:
The discriminant (\( \Delta \)) of a quadratic equation \( ax^2 + bx + c = 0 \) is given by the formula:
\[ \Delta = b^2 - 4ac \]
#### Explanation:
1. **Identify the coefficients:**
- \( a = 3 \)
- \( b = -8 \)
- \( c = 2 \)
2. **Calculate the discriminant:**
\[ \Delta = (-8)^2 - 4(3)(2) \]
\[ \Delta = 64 - 24 \]
\[ \Delta = 40 \]
#### Result:
- **Discriminant:** \( \Delta = 40 \)
- **Number & type of solutions:**
- Since \( \Delta > 0 \), there are **two distinct real solutions**.
### Summary:
The provided quadratic equation has a discriminant of 40, indicating that it has two distinct real solutions. By analyzing the discriminant value, one can determine the nature and number of solutions for any quadratic equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a15d03a-cf19-479c-9f1f-b178583254bd%2F18d49a23-ec50-4fa3-a8ae-c908f8c3e18c%2Fbafsymi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Quadratic Equation Discriminant Analysis
#### Problem Statement:
11) For the following equation, use the discriminant to determine the number and type of solutions.
\[ y = 3x^2 - 8x + 2 \]
#### Formula:
The discriminant (\( \Delta \)) of a quadratic equation \( ax^2 + bx + c = 0 \) is given by the formula:
\[ \Delta = b^2 - 4ac \]
#### Explanation:
1. **Identify the coefficients:**
- \( a = 3 \)
- \( b = -8 \)
- \( c = 2 \)
2. **Calculate the discriminant:**
\[ \Delta = (-8)^2 - 4(3)(2) \]
\[ \Delta = 64 - 24 \]
\[ \Delta = 40 \]
#### Result:
- **Discriminant:** \( \Delta = 40 \)
- **Number & type of solutions:**
- Since \( \Delta > 0 \), there are **two distinct real solutions**.
### Summary:
The provided quadratic equation has a discriminant of 40, indicating that it has two distinct real solutions. By analyzing the discriminant value, one can determine the nature and number of solutions for any quadratic equation.
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