Practice - Nature of Roots Using Discriminant
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Practice Questions
Test your understanding with targeted questions
Calculate the discriminant for the equation x² + x + 1 = 0.
💡 Hint: Remember to use the formula D = b² - 4ac.
What is the nature of the roots for the equation 2x² - 4x + 2 = 0?
💡 Hint: Calculate the discriminant using the provided coefficients.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What happens if the discriminant D is greater than 0?
💡 Hint: Think about the nature of different root situations in relation to the graph.
True or False: If D = 0, the equation has complex roots.
💡 Hint: Consider what it means for points to be equal on the graph.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
For a quadratic equation represented by ax² + (k-1)x + (k-3) = 0, where k is a parameter, determine the value(s) of k that lead to complex roots.
💡 Hint: Start by calculating the discriminant.
Prove that the roots are real if and only if the quadratic is represented by the inequality a(b² - 4ac) > 0.
💡 Hint: Analyze the definitions of each scenario and ensure you refer back to the discriminant.
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