Practice Cases Based on Nature of Roots - 3.3 | 3. Second-Order Homogeneous Equations with Constant Coefficients | Mathematics (Civil Engineering -1)
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Cases Based on Nature of Roots

3.3 - Cases Based on Nature of Roots

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the general solution for an equation with distinct real roots?

💡 Hint: Think about the terms that depend on r.

Question 2 Easy

Identify the nature of roots when D = 0.

💡 Hint: What does a zero determinant indicate?

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does a positive discriminant indicate about the roots?

Complex roots
Repeated roots
Distinct real roots

💡 Hint: Think about how the graph of a quadratic opens.

Question 2

True or False: A repeated root leads to a solution with linear terms.

True
False

💡 Hint: Consider how double roots affect the quadratic’s graph.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the equation y'' + 4y' + 4y = 0, find the roots and classify them. What is the general solution?

💡 Hint: Use the quadratic formula and consider special cases for roots.

Challenge 2 Hard

Solve and find the nature of roots for: y'' - y = 0. Derive the general solution.

💡 Hint: Identify the discriminant first!

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