Math Problem Statement
how to solve this?
Solution
The equation you are solving in the image is a quadratic equation:
You correctly identified the coefficients:
The next step is to apply the quadratic formula:
Substitute the values , , and into the formula:
This simplifies to:
Now, you encounter a square root of a negative number, , which implies that the solutions are complex numbers. In complex numbers, , where is the imaginary unit. Therefore:
Now substitute this back into the formula:
Simplify:
Thus, the two complex solutions are:
These are the final solutions to the quadratic equation.
Would you like any further explanation or details on this?
Here are five related questions that expand upon this topic:
- What are the conditions for a quadratic equation to have real vs complex solutions?
- How do you graph quadratic equations with complex solutions?
- Can the discriminant () predict the nature of the roots?
- How do imaginary numbers like behave in calculations involving powers?
- What are the applications of complex numbers in physics or engineering?
Tip: The discriminant () is key to knowing whether your quadratic has real or complex solutions.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Complex Numbers
Formulas
Quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a
Theorems
Quadratic formula
Discriminant for determining real or complex roots
Suitable Grade Level
Grades 9-12
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