Equation

Definition: An equation is a relation between two algebraic expressions symbolized by the sign of equality (=).
For example the equation 
     3x + 5 = 2x + 7
is true only for x = 2 and not foe x = 3.



Question: Write the nature of roots of quadratic equation   

Solution: Since the roots of the quadratic equation    

              

are given by    

               

The nature of roots shall depend on the   b² - 4ac   (where a, b, c are real and rational), generally it is denoted by Δ , 

We obtain the following results

1. If  Δ  >  0 and is a perfect square then the roots are rational and unequal.
2. If  Δ  >  0 but not a perfect square then the roots are irrational and unequal.
3. If  Δ  =  0 then the roots are real and equal.
4. If  Δ <  0 then the roots are complex and imaginary.