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The zero Principles of the Quadratic Equations - Homework | MTH 65, Assignments of Algebra

Material Type: Assignment; Class: Introductory Algebra-2nd Term; Subject: Math; University: Portland Community College; Term: Spring 2008;

Typology: Assignments

Pre 2010

Uploaded on 08/19/2009

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MTH 65 – Mr. Simonds’ class
Page 1 of 8
Key Concepts: Quadratic Equations
The zero principle
Yippe-ay-yay... word problems!!
Martin-Gaye practice problems: Section 6.5: 1 – 69 odd
Section 6.6: 1 15 odd, 25 39 odd, 59
Examples
Find the solutions to the equation
()
(
)
38570xx
+
−=
.
Solve the equation
()
60.xx
=
Solve the equation
()
6 10.xx−=
The zero principle
If
0ab=
, then
0a
=
and/or
0b
=
.
pf3
pf4
pf5
pf8

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Key Concepts: Quadratic Equations The zero principle Yippe-ay-yay... word problems!!

Martin-Gaye practice problems: Section 6.5: 1 – 69 odd Section 6.6: 1 – 15 odd, 25 – 39 odd, 59

Examples

Find the solutions to the equation ( 3 x + 8 )( 5 x − 7 )= 0.

Solve the equation x x ( − 6 ) =0.

Solve the equation x x ( − 6 ) =10.

The zero principle

If a b = 0 , then a = 0 and/or b = 0.

Find the solutions to the equation x^3^ + 3 x^2 − x = 3

The zero principle

  • Remember, it’s the zero principle. You cannot use the principle unless one side of the equation is zero.
  • Remember, the principle says that if two expressions are multiplied and the result is zero, the value of at least one of the expressions must be zero. The principle cannot be applied unless the non-zero side of the equation is completely factored.

Quadratic Equations

Equations that can be written in the form a x^2 + b x + c = 0, a ≠ 0 are called quadratic equations. The form a x^2^ + b x + c = 0 is called the standard form of a quadratic equation.

A strategy for solving quadratic equations

  1. Write the equation in standard form. This sometimes requires expanding the product of two binomials not equal to zero.
  2. Factor the non-zero side of the equation and apply the zero principle.

( x − 10 )( x + 1 ) = − 10

7 ( x − 8 ) = 4 − ( x − 8 )

0 = 36 t^2 − 12 t − 35

A bean bag is thrown into the air from the top of a 168 ft building with an initial velocity of 88 ft/s. It can be shown using calculus that the height of the bag (ft) t seconds after it is shot is given by

the function h t ( ) = − 16 t^2 + 88 t + 168. Find the number of seconds it takes for the bag to fall to

the ground.

Swing your partner, ‘cuz it’s hoe-down time at the Shady Proprietors Retirement Home – the monthly Ronald Reagan memorial square dance, to be precise. There’s some serious dosadoing going on, and at the end of the spins each side of the square is 2 ft wider than it was before the call to dosado. The area of the new square is 484 ft 2. What was the area of the square before the dosadoing began?

Dr. Dieter has a pool in her backyard that is in the shape of an isosceles right triangle! The pool sits in a square tiled walkway as illustrated below. The total area of the pool area (including the walkway) is 2025 ft^2. How long is each side of Dr. Dieter’s triangular pool?

5 ft

5 ft

5 ft 5 ft

Velma Smeltz invested all of her bingo winnings in a government bond. The bond earns an annual interest rate, r , that is applied at the end of each year. The amount of money, A , in Velma’s

account at the end of the t th^ year is given by the formula 175 1( )

t A = + r. At the end of the

second year there was $196.63 in the account. What is the annual interest rate on the account?