Question

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

Answer 1

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