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When using the rational root theorem, which of the following is a possible root of the polynomial function below? F(x) = 3x - x2 + 4x +5 ОА. б O B. -7 Ос O C. - D.

When Using The Rational Root Theorem Which Of The Following Is A Possible Root Of The Polynomial Function Below Fx 3x X2 4x 5 ОА Б O B 7 Ос O C D class=

Sagot :

Given:

[tex]f(x)3x^3-x^2+4x+5[/tex]

Since all coefficients are integers, we can apply the rational zeros theorem

The coefficient of the constant term is 5

The factors of 5 are +1, -1, +5, -5

These are the possible values for p

[tex]p=\pm1,\pm5[/tex]

The leading coefficient (the coefficient of the term with the highest degree) is 3

The factors of 3 are +1, -1, +3, -3

These are the possible values for q

[tex]q=\pm1,\pm3[/tex]

The possible rational roots are

[tex]\frac{p}{q}=\pm1\pm\frac{1}{3},\pm5,\pm\frac{5}{3}_{}[/tex]

From the options provided the possible rational root is

-5/3, OPTION C

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