According to the Rational Root Theorem, which statement about f (x) = 66x4 - 2x3 + 11x2 + 35 is true? Any rational root of f (x) is a factor of 35 divided by a factor of 66. Any rational root of f (x) is a multiple of 35 divided by a multiple of 66. Any rational root of f (x) is a factor of 66 divided by a factor of 35. Any rational root of f (x) is a multiple of 66 divided by a multiple of 35.

Question

Mathematics

Tania Wall

9 April, 02:57

According to the Rational Root Theorem, which statement about f (x) = 66x4 - 2x3 + 11x2 + 35 is true? Any rational root of f (x) is a factor of 35 divided by a factor of 66. Any rational root of f (x) is a multiple of 35 divided by a multiple of 66. Any rational root of f (x) is a factor of 66 divided by a factor of 35. Any rational root of f (x) is a multiple of 66 divided by a multiple of 35.

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Cooper Hurst · Answer 1

The correct statement is any rational root of f (x) is a factor of 35 divided by a factor of 66

Step-by-step explanation:

The correct option is Any rational root of f (x) is a factor of 35 divided by a factor of 66

The Rational root theorem states that If f (x) is a Polynomial with integer coefficients and if there exist a rational root of the form p/q then p is the factor of the constant term of the function and q is the factor of the leading coefficient of the function.

f (x) = 66x4 - 2x3 + 11x2 + 35

Here 66 is the factor of the leading coefficient (q)

and 35 is the factor of the constant term (p)

Thus p/q = 35/66

Therefore the correct statement is any rational root of f (x) is a factor of 35 divided by a factor of 66 ...