Download Quadratic Formula and the Number of Real Zeros

QUADRATIC FORMULA
Quadratic Formula provides solutions to a quadratic equation, i.e. provides values for the
zeros of a quadratic function.
f ( x)
b
x1
b2
2a
Let’s introduce a symbol
ax 2
4ac
bx c
x2
0
b
b2
2a
4ac
b2
(read: delta) to denote a discriminant
4ac
It determines the number of real solutions of a quadratic equation.
y
0
x
No real solutions.
X1 and X2 are complex numbers (non-real).
______________________________________________________________________
0
y
One real solution.
x
X1 = X2 is a real number.
______________________________________________________________________
0
y
Two real solutions.
x
X1
X2 are real numbers.
By Joanna Gutt-Lehr, Pinnacle Learning Lab, last updated 1/2007