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According to the rational root theorem, which of the following are possible
roots of the polynomial function below?
F(x) = 4x2 - 6x2 + 9x + 10

A.5/4
B.1/3
C.-1/2
D.5
E.6
F.-2


According To The Rational Root Theorem Which Of The Following Are Possible Roots Of The Polynomial Function Below Fx 4x2 6x2 9x 10 A54 B13 C12 D5 E6 F2 class=

Sagot :

Given:

The polynomial function is

[tex]F(x)=4x^3-6x^2+9x+10[/tex]

To find:

The possible roots of the given polynomial using rational root theorem.

Solution:

According to the rational root theorem, all the rational roots and in the form of [tex]\dfrac{p}{q}[/tex], where, p is a factor of constant and q is the factor of leading coefficient.

We have,

[tex]F(x)=4x^3-6x^2+9x+10[/tex]

Here, the constant term is 10 and the leading coefficient is 4.

Factors of constant term 10 are ±1, ±2, ±5, ±10.

Factors of leading term 4 are ±1, ±2, ±4.

Using rational root theorem, the possible rational roots are

[tex]x=\pm 1+,\pm 2, \pm 5, \pm 10,\pm \dfrac{1}{2}, \pm \dfrac{5}{2}, \dfrac{1}{4}, \pm \dfrac{5}{4}[/tex]

Therefore, the correct options are A, C, D, F.