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