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

Try these first

1. 1.

   What is the discriminant of the equation r² − 5r + 6 = 0?

   Hint

   Calculate using D = b² - 4ac.

2. 2.

   List the general form of the solution for distinct roots.

   Hint

   Consider the forms based on the root types.

3. 3.

   What does a positive discriminant indicate about the roots of a quadratic equation?

   • True
   • False

   Hint

   Think about how the discriminant is calculated.

4. 4.

   Which condition indicates a case with distinct roots?

   • D < 0
   • D = 0
   • D > 0

   Hint

   Recall the formula for the discriminant.

5. 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.

   Hint

   Determine the discriminant and use complex root formulas.

6. 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.

   Hint

   Utilize initial conditions to form a system of equations.