The Rational Root Theorem states that any rational solution of a polynomial equation, in the form of p/q, must have p as a factor of the constant term and q as a factor of the leading coefficient. So, if we consider 7/8 as a potential rational root, we need to find a polynomial function that fits this description.
To construct such a function, let’s say we take a polynomial of the simplest form:
f(x) = 8x - 7In this case, if we substitute x = 7/8 into the function:
f(7/8) = 8(7/8) - 7 = 7 - 7 = 0This shows that 7/8 is indeed a root of the polynomial function f(x) = 8x – 7. Any polynomial that has 7/8 as a root will have similar properties, where its leading coefficient and constant term are appropriate multiples of 8 and -7 respectively.