3.3. Cases Based on Nature of Roots

Try these first

1. 1.

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

   Hint

   Think about the terms that depend on r.

2. 2.

   Identify the nature of roots when D = 0.

   Hint

   What does a zero determinant indicate?

3. 3.

   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.

4. 4.

   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.

5. 5.

   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.

6. 6.

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

   Hint

   Identify the discriminant first!