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Chapter 5

Polynomial Equations of the Second Degree

 
 
5.3 Examples

Example 1

Solve the following equations:

(i)     (ii)     (iii) 

Solution

(i) It is and the equation has two distinct solutions:
  and 
(ii) In a similar way we have D=0 and a double solution 
(iii) It is and the therefore the equation has no solution in R but it has two complex solutions.  and 
Example 2

Prove that the equation  has two real distinct solutions.

Solution

It is 

for every .

Example 3

Find three consecutive odd numbers such as the sum of their squares to be equal to 83.

Solution

Let 2v+1, 2v+3, 2v+5 be the three consecutive odd numbers (v belongs to Z).
We have:



 v = - 4 or v=1