Quadratic Equations

Date: 6/25/96 at 18:36:45
From: Sandi Pohlmann
Subject: Quadratic Equations 

Use the zero-factor property to solve.

(2a-5)(a+3) = 0.
     z(z-7) = 0.

Solve each equation by the square root property.

        p^2 = 16.

Solve each equation by using the quadratic formula.

q2 - 7q + 6 = 0.

Thank you.

Date: 6/26/96 at 10:4:34
From: Doctor Jerry
Subject: Re: Quadratic Equations 

1. This is in the form of a product of two numbers.  The zero-factor 
property is the fact that if the product of two numbers is zero, then 
at least one of them must be zero.  So, either 2a-5 = 0 or a+3 = 0.  
Solving these simpler equations gives a = 5/2 or a = -3.  So, if a is 
either of these values, the equation is satisfied.

2. Using the same property, z = 0 or z = 7.

3. So, if p^2 = 16, then p is a number whose square is 16.  Thus 
p must be either 4 or -4, which are the square roots of 16.

4. For ax^2 + bx + c = 0, the quadratic formula is -b +- sqrt(b^2-4ac)
                                                   ------------------
                                                           2a

The sign +- means plus or minus.  Just substitute, a = 1, b = -7, and 
c = 6.  This gives -(-7) +- sqrt[49-4(1)(6)]
                   ------------------------- .
                             (2)  


This simplies to  7 +- sqrt(25)   or (7+5)/2 and (7-5)/2 or 6 and 1.
                 --------------
                        2 

Good luck.

-Doctor Jerry,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/