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# A. Use the fundamental theorem of algebra to determine the number of roots for 2x^2+4x+7

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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

Guest Oct 26, 2017
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Because the degree is two, we either have two real roots or two complex roots

The roots are non-real because the discriminant is < 0

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

2x^2  +  4x  = -7

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, simplify the right

(x + 1) ^2  =  -5/2       take both roots

x + 1  =  ± √[ -5/2 ]    subtract 1  and simplify the right

x  = ± √[5/2] i    - 1

CPhill  Oct 26, 2017

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