Practice Cases Based On Nature Of Roots (3.3) - Second-Order Homogeneous Equations with Constant Coefficients

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8 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the general solution for an equation with distinct real roots?
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Think about the terms that depend on r.
Question 2.
Identify the nature of roots when D = 0.
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What does a zero determinant indicate?
3Question 3.
What does a positive discriminant indicate about the roots?
- Complex roots
- Repeated roots
- Distinct real roots
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Think about how the graph of a quadratic opens.
4Question 4.
True or False: A repeated root leads to a solution with linear terms.
- True
- False
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Consider how double roots affect the quadratic’s graph.
Question 5.
Given the equation y'' + 4y' + 4y = 0, find the roots and classify them. What is the general solution?
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Use the quadratic formula and consider special cases for roots.
Question 6.
Solve and find the nature of roots for: y'' - y = 0. Derive the general solution.
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Identify the discriminant first!

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