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(a)  Use the fundamental theorem of algebra to determine the number of roots for  .

(b)  What are the roots of ? Show your work.

 

SamJones  Feb 7, 2018
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a. The fundamental theorem says that a polynomal of degree "n"   will have "n" roots

 

Note that some may be repeated  and/or some may be complex

 

So.....this a polynomial of degree 2....so...it will have two roots

 

b.

 

2x^2 + 4x + 7  =  0      

 

Use the quadratic formula   a = 2, b = 4, c = 7

 

So we have

 

x1,2  =  [  - 4 ± √ [4^2 - 4(2)(7) ] ]  /  [ 2 * 2 ]  =

 

[  -4 ± √ [ 16 - 56]  ]  / 4  =

 

[ -4 ± √ -40 ] / 4  =

 

[ - 4 ± 2i√ 10 ] / 4  =

 

[ -2 ± i√ 10 ] / 2

 

 

cool cool cool

CPhill  Feb 7, 2018

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