Download 6.10 The Discriminant

6.10 THE DISCRIMINANT
THE DISCRIMINANT

The discriminant is part of the quadratic
formula.
b  4ac
2

The discriminant is used to determine the nature
of the solutions of a quadratic equation.
THE NATURE OF THE SOLUTIONS
Value of the Discriminant
Nature of the Solutions
<0
No real solutions
=0
One Solution; Real, Rational
> 0 and a perfect square
Two Solutions; Real, Rational
> 0 and not a perfect square
Two Solutions, Real, Irrational
EVALUATE AND WRITE THE
DISCRIMINANT. THEN DESCRIBE
THE SOLUTIONS.
5 x  8 x  11  0
2
EVALUATE AND WRITE THE
DISCRIMINANT. THEN DESCRIBE
THE SOLUTIONS.
6 x  10 x  2  0
2
EVALUATE AND WRITE THE
DISCRIMINANT. THEN DESCRIBE
THE SOLUTIONS.
15 x 2  7 x  2  0
EVALUATE AND WRITE THE
DISCRIMINANT. THEN DESCRIBE
THE SOLUTIONS.
10 x  11x  4  10
2
EVALUATE AND WRITE THE
DISCRIMINANT. THEN DESCRIBE
THE SOLUTIONS.
1  0.8 x  1.6 x 2
FIRE HOSE PROBLEM

Water comes out of a fire hose with a velocity
of 23 meters per second. If the hose is aimed
straight up, will the water reach:
a)
b)
The fifth story, 25 meters up?
The sixth story, 30 meters up?
HOMEWORK

P 261 #1 – 33 odd, 35, and 36