Squaring Off Using Quadratic Equations

A quadratic equation has a squared term in it. For instance,x2 + 2x-3 = 0isa quadratic equation. An interesting feature of these equations is that many quadratic equations have two completely different solutions. In the equation x2 + 2x - 3 = 0, x is equal to either +1 or -3. Either number works. Number problems using quadratic equations in their solutions may or may not use both answers. After solving the problem, you go back and look at the original question to see if both answers make sense. 

Stefanie was hired to paint the numbers on the How many times did Stefanie have to paint the 

Number problems that need two answers or end up with two solutions have to be checked carefully. The equations used when solving these number problems frequently involve expressions relating one of the numbers to the other number using mathematical operations. 

The Problem The sum of a number and eight times its reciprocal is 6. What are the two numbers  

First write expressions for the number and its reciprocal. Letting x be the number, then its reciprocal is j -. Multiplying that reciprocal by 8, 8 j = Now write an equation that represents the sentence exactly. The word sum indicates that the number and its reciprocal are added. The word is indicates 

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