6
QuizMultiple Choice

The Rational Roots Theorem — Quiz

Question 6 • Mathematics III

According to the Rational Root Theorem, negative 7 eighths is a potential rational root of which function?

Answer
A
f of x is equal to 28 x to the 7th power plus 3 x to the 6th power plus 4 x cubed minus x minus 24
B
f of x is equal to 56 x to the 7th power plus 3 x to the 6th power plus 4 x cubed minus x minus 30
C
f of x is equal to 30 x to the 7th power plus 3 x to the 6th power plus 4 x cubed minus x minus 56
D
f of x is equal to 24 x to the 7th power plus 3 x to the 6th power plus 4 x cubed minus x minus 28

Explanation

By the Rational Root Theorem, a reduced fraction p/q can be a rational root only if p divides the constant term and q divides the leading coefficient. For −7/8, 7 must divide the constant term and 8 must divide the leading coefficient. In choice A, the constant term is −28 and the leading coefficient is 24; 7 divides −28, and 8 divides 24. So choice A meets both requirements.

AI-written and checked against the verified answer.

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