The polynomial function f(x)=10x^6+7x-7 is graphed below

according to the rational roots theorem which is a possible root at point p

a. the root at point p may be 5/7
b. the root at point p may be 2/7
c. the root at point p may be 7/10
d. the root at point p may be 10/7

Option c

Step-by-step explanation:

Please see the attached picture for the graph of the polynomial.

According to the rational roots theorem, the leading coefficient of the polynomial (an) must be divisible by the denominator of the fraction and the constant term (a0) must be divisible by the numerator of the rational root (p/q).

Where the polynomial is defined as

an*x^n + (an-1)*x^(n-1) + ...+  (a1)*x^(1) +  (a0) = 0

In this case, the leading coefficient is divisible by 1,2,5 10

and the constant term is divisible by 1,7

if any rational roots exist, they must have a denominator of 1,2,5 10 and a numerator of 1,7

So the correct answer is option c