Which of the following is NOT a possible root of the function? (Hint: Use the rational root theorem, write out all the possible roots, and see which one is NOT on your list.) Please use any sources to help you. f(x)= 3x^3+2x^2+x+4

A. +4/3
B. +1
C. +3/4
D. +2

Given:

The function is

To find:

The value from the given options that is NOT a possible root of the function.

Solution:

According to rational root theorem, all possible roots are in the form of

We have,

Here,

Leading coefficient = 3.

Constant term = 4

Factors of 3 are ±1, ±3.

Factors of 4 are ±1, ±2, ±4.

Using rational root theorem, all possible roots of given functions are

Clearly, are possible roots but is not the possible root.

Therefore, the correct option is C.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

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step-by-step explanation:

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