Why does the discriminant determine how about solutions there can be?

Question

Where can we find the discriminant?

Answer 1

 

 Because discriminant is argument of a radical, and the roots can be rational, irrational or complex number, according to value of discriminant be , perfect square, not a perfect square or negative.

 

 Discriminant is b² - 4ac in a quadratic in the form of aX² + bx + c.

  It comes up in quadratic equation.

 

    Given : aX²+ bx + c = 0    to solve for x

 

                X² + b/a X + C/a = 0

 

               X²+ 2 b/2a + b² /(4a²) = -C/a + b²/4a²

               

                (  X + b/ 2a) ² = (( b² - 4ac)/4a²

               

                 X + b/2a =± √(b²-4ac) /2a

 

                  X = - b/2a ± √(b²- 4ac) / 2a