Practice Case 1: Distinct Real Roots (d =b²−4ac>0) (3.3.1) - Second-Order Homogeneous Equations with Constant Coefficients

Practice: Case 1: Distinct Real Roots (D =b²−4ac>0)

Lesson 3.3.1Second-Order Homogeneous Equations with Constant Coefficients

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6 sample questions

Question 1.
What is the discriminant of the equation r² − 5r + 6 = 0?
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Calculate using D = b² - 4ac.
Question 2.
List the general form of the solution for distinct roots.
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Consider the forms based on the root types.
3Question 3.
What does a positive discriminant indicate about the roots of a quadratic equation?
- True
- False
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Think about how the discriminant is calculated.
4Question 4.
Which condition indicates a case with distinct roots?
- D < 0
- D = 0
- D > 0
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Recall the formula for the discriminant.
Question 5.
A second-order differential equation y'' + 4y' + 5y = 0 has roots that are not distinct. Solve for the roots and find the general solution.
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Determine the discriminant and use complex root formulas.
Question 6.
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.
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Utilize initial conditions to form a system of equations.

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