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1. (a)  Use the fundamental theorem of algebra to determine the number of roots for  2x^2+4x+7.

    (b)  What are the roots of 2x^2+4x+7? Show your work.

 

2. Consider the function f=(x)=x^3+2x^2-3 .

    Graph the function.

    What are the x- and y-intercepts of the graph?

 

3. Simplify the expression (x^3-5x^2+7x-12)÷(x-4) using long division. Show your work.

oscar.a1551  Nov 1, 2018
 #1
avatar+91213 
+2

1)  (a)  There will be as many roots of a polynomial as its degree  [  some may be repeated roots ]

So....the number of roots here    = 2    since this is a second degree polynomial

 

(b)   2x^2 + 4x + 7  = 0     subtract 7 from both sides

 

2x^2 + 4x  =  - 7      factor out the 2 on the left

 

2 ( x^2 + 2x )   =  - 7    divide both sides by 2

 

x^2 + 2x  =  -7/2  

 

Take 1/2 of 2  = 1...square it = 1....add it to both sides

 

x^2 + 2x + 1   =  -7/2 + 1      factor the left side, simplify the right

 

(x + 1)^2  = -5/2     take both roots

 

x + 1  =  ±√ [ - 5/2]  =  ±i √ 5 / √2  =   ±i √10 /2

 

x + 1  = ±i√10 / 2    subtract 1 from both sides

 

x =  -1 ±i√10 / 2

 

x =  [  -2  ± i √10 ]  / 2

 

 

cool cool cool

CPhill  Nov 1, 2018
edited by CPhill  Nov 1, 2018
 #2
avatar+91213 
+2

2)  Here's the graph : https://www.desmos.com/calculator/hz0nsgeb2n

 

The x intercept   is  (1, 0)

The y intercept is (0, - 3)

 

 

cool cool cool

CPhill  Nov 1, 2018
 #3
avatar+91213 
+2

(x^3-5x^2+7x-12)÷(x-4)

 

 

             x^2   -  x    +  3

x - 4  [  x^3  -5x^2  + 7x  -  12  ]

            x^3 - 4x^2

          ______________________

                  - x^2  +  7x

                  - x^2  + 4x

                __________________

                            3x   -   12

                            3x   -   12

                          __________

 

The result is in red

 

 

 

 

cool cool cool

CPhill  Nov 1, 2018

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