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Q. Quadratic equation for
- Identify Coefficients: Step Title: Identify the CoefficientsConcise Step Description: Identify the coefficients of the quadratic equation, which are the numbers in front of the variables. In this case, the coefficients are , , and .Step Calculation: Coefficients are , , Step Output: Coefficients: , ,
- Calculate Discriminant: Step Title: Calculate the DiscriminantConcise Step Description: Calculate the discriminant of the quadratic equation using the formula , where , , and are the coefficients identified in the previous step.Step Calculation: Step Output: Discriminant:
- Check Roots Nature: Step Title: Check the Nature of the RootsConcise Step Description: Check the nature of the roots using the discriminant. If the discriminant is positive, there are two real and distinct roots. If it is zero, there is one real root. If it is negative, there are two complex roots.Step Calculation: Since the discriminant is , which is less than zero, the roots are complex.Step Output: Nature of the Roots: Complex
- Apply Quadratic Formula: Step Title: Apply the Quadratic FormulaConcise Step Description: Apply the quadratic formula to find the roots of the equation. The quadratic formula is , where is the discriminant.Step Calculation: Step Output: Roots:
- Simplify Complex Roots: Step Title: Simplify the Complex RootsConcise Step Description: Simplify the complex roots by writing the square root of the negative discriminant as the product of (the imaginary unit) and the square root of the positive part of the discriminant.Step Calculation: Step Output: Simplified Roots:
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