Solutions to Quadratic Equations
ax2 + bx +c = 0
b2 − 4ac is called the discriminant of the quadratic equation and determines the number of solutions in each equation. Three cases can be distinguished:
b2 − 4ac > 0
In this case, the quadratic equation has two solutions, which are distinct real numbers.
b2 − 4ac = 0
In this case, the quadratic equation has a double solution.
b2 − 4ac < 0
In this case, the quadratic equation has no real solutions.
Properties of the Solutions to Quadratic Equations
The sum of the solutions of a quadratic equation is:
The product of the solutions of a quadratic equation is:
Quadratic Equation from Solutions
If the roots of an equation are known, it can be writen as:
Where:
S = x1 + x2
P = x1 · x2
Write a quadratic equation whose solutions are: 3 and −2.
S = 3 − 2 = 1
P = 3 · (−2) = −6
x2 − x − 6 = 0
