(a) use the fundamental theorem of algebra to determine the number of roots for 2x^2+4x+7 show your work
(b) what are the roots of 2x^2+4x+7 show your work.

The answer to your question is: This polynomial does not have root, it does not intercept the x-axis.

Step-by-step explanation:

a)

                                             2x² + 4x + 7

To determine the number of roots of this polinomial, just look at the higher power and that number will be the maximum possible number of roots.

In this exercise, the maximum power is 2, so this polynomial could have at most 2 roots.

b) Find the possible roots of the polynomial, which are multiples of 7

   Possible roots:  ±1, ±7

                                             2x² + 4x + 7

Use synthetic division to find the roots

                                   2     4     7       1

                                          2     6                              

                                   2     6    13                   +1 is not a root

                                   2    4     7        -1

                                        -2    -2                  

                                   2    2    5                    -1 is not a root

                                  2     4     7         7

                                         14   126                  

                                  2     18  133                  +7 is not a root

                                  2     4     7        -7

                                        -14   70                  

                                  2    -10   -77              -7 is not a root

18a

step-by-step explanation:

simply because it is. it's the highest common factor