3.3.1 - Case 1: Distinct Real Roots (D =b²−4ac>0)
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Practice Questions
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What is the discriminant of the equation r² − 5r + 6 = 0?
💡 Hint: Calculate using D = b² - 4ac.
List the general form of the solution for distinct roots.
💡 Hint: Consider the forms based on the root types.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does a positive discriminant indicate about the roots of a quadratic equation?
💡 Hint: Think about how the discriminant is calculated.
Which condition indicates a case with distinct roots?
💡 Hint: Recall the formula for the discriminant.
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Challenge Problems
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A second-order differential equation y'' + 4y' + 5y = 0 has roots that are not distinct. Solve for the roots and find the general solution.
💡 Hint: Determine the discriminant and use complex root formulas.
Given y'' - 7y' + 10y = 0, find the general solution and use initial conditions y(0)=2, y'(0)=5 to find specific values for constants.
💡 Hint: Utilize initial conditions to form a system of equations.
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