Question

According to the Rational Roots Theorem, which statement about f(x) = 25x7 – x6 – 5x4 + x – 49 is true? Any rational root of f(x) is a multiple of –49 divided by a multiple of 25. Any rational root of f(x) is a multiple of 25 divided by a multiple of –49. Any rational root of f(x) is a factor of –49 divided by a factor of 25. Any rational root of f(x) is a factor of 25 divided by a factor of –49.

Answer 1

Answer:

Any rational root of f(x) is a factor of -49 divided by a factor of 25

Step-by-step explanation:

The Rational Roots Theorem states that, given a polynomial

$p(x) = a_nx^n+a_{n-1}x^{n-1}+\ldots+a_2x^2+a_1x+a_0$

the possible rational roots are in the form

$x=\dfrac{p}{q},\quad p\text{ divides } a_0,\quad q\text{ divides } a_n$

Answer 2

The rational root theorem is used to determine the possible roots of a function.

The true statement about $f(x) = 25x^7 - x^6 - 5x^4 + x - 49$ is (c) Any rational root of f(x) is a factor of =-49 divided by a factor of 25.

For a rational function,

$f(x) = px^n + ax^{n-1} + ...................... + bx + q$

The potential roots by the rational root theorem are:

$Roots = \pm\frac{Factors\ of\ q}{Factors\ of\ p}$

By comparison,

p = 25, and q = -49

So, we have:

$Roots = \pm\frac{Factors\ of\ -49}{Factors\ of\ 25}$

Hence, the true statement about $f(x) = 25x^7 - x^6 - 5x^4 + x - 49$ is (c)

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