Number of Solutions (Roots) of a Quadratic Equation

The number of solutions for a quadratic equation depends on the value of the discriminant in the quadratic formula .

1. If , the equation has two distinct roots. solutions
2. If , the equation has one repeated root (double root). solution
3. If , there are no real roots. solutions

The equation has real solutions if .
For a quadratic equation of the form , where the coefficient of is even, you can use instead of .
Summary of the Number of Solutions Based on

Sign of	Quadratic Equation Solutions	Number of Distinct Roots
	or	2
	No real roots (no square root of a negative number)