Consider the generic form of a quadratic equation, i.e. ax^2 + bx + c = 0 where a ̸= 0

Question

Consider the generic form of a quadratic equation, i.e. ax^2 + bx + c = 0 where a ̸= 0. Often there are two distinct roots to a quadratic equation. Explain how many distinct roots there are if b2 = 4ac and why.

Answer 1

Hi,

ax^2 + bx + c = 0, for finding the solution of this equation by quadratic formula you need to know the quadratic formula x₁, x_{2 = ( -b ±√} b² - 4ac ) / 2a that depends of sign b^2 -4ac

1) b² - 4ac > 0 in this case you have two real numbers as a solution x₁, x_{2 = ( -b ±√} b² - 4ac ) / 2a

2) b² - 4ac = 0 in this case you have one number (multiplicity 2 ) x = -b /2a

3) b² - 4ac <0 in this case there is no real number because under the radical is negative BUT there are two complex numbers that it is out of this subject.

I hope it is useful,

Minoo

Answer 2

In the Quadratic Formula b² - 4ac is the argument of the radical.

if b² = 4ac then the argument = 0.

The two solutions are identical.