Math Problem Statement
How do you find the root of -x²-4x+5
Solution
To find the roots of the quadratic equation , you can either factor the equation or use the quadratic formula. Since this equation does not factor easily, let's use the quadratic formula:
The quadratic formula is: where , , and are the coefficients of the quadratic equation . For the given equation , we have:
- (coefficient of ),
- (coefficient of ),
- (constant term).
Step-by-step solution:
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Substitute , , and into the quadratic formula:
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Simplify the expression:
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Solve the square root of 36:
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Find the two possible solutions:
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First solution:
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Second solution:
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The roots are:
Let me know if you'd like more details or have any questions!
Here are 5 related questions to expand your understanding:
- How would the quadratic formula change if were positive?
- How do you determine the nature of the roots using the discriminant?
- Can you solve this quadratic equation by completing the square?
- What does the graph of look like?
- How would you solve (an inequality)?
Tip: Always check the discriminant before solving a quadratic equation. It tells you how many and what kind of roots you will get!
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Roots of Equations
Formulas
Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a
Theorems
Quadratic Formula
Discriminant Analysis
Suitable Grade Level
Grades 8-10