According to the rational root theorem, the following are potential roots of f(x) = 6x4 + 5x3 – 33x2 – 12x + 20. -5/2,-2, 1, 10/3 which is an actual root of f(x)?

The actual root of f(x) is -5/2 (first option)

Step-by-step explanation:

A root of f(x) is a value of the variable "x" that makes f(x)=0

1) With x=-5/2

f(-5/2)=6(-5/2)^4+5(-5/2)^3-33(-5/2)^2-12(-5/2)+20

f(-5/2)=6(5^4/2^4)+5(-5^3/2^3)-33(5^2/2^2)+6(5)+20

f(-5/2)=6(625/16)-5(125/8)-33(25/4)+30+20

f(-5/2)=3(625/8)-625/8-825/4+50

f(-5/2)=1,875/8-625/8-825/4+50

f(-5/2)=[1,875-625-2(825)+8(50)]/8

f(-5/2)=(1,875-625-1,650+400)/8

f(-5/2)=0/8

f(-5/2)=0 then x=-5/2 is a root of f(x)

2) With x=-2

f(-2)=6(-2)^4+5(-2)^3-33(-2)^2-12(-2)+20

f(-2)=6(2^4)+5(-2^3)-33(2^2)+24+20

f(-2)=6(16)-5(8)-33(4)+44

f(-2)=96-40-132+44

f(-2)=-32 different of 0, then x=-2 is not a root of f(x)

3) With x=1

f(1)=6(1)^4+5(1)^3-33(1)^2-12(1)+20

f(1)=6(1)+5(1)-33(1)-12+20

f(1)=6+5-33+8

f(1)=-14 different of 0, then x=1 is not a root of f(x)

4) With x=10/3

f(10/3)=6(10/3)^4+5(10/3)^3-33(10/3)^2-12(10/3)+20

f(10/3)=6(10^4/3^4)+5(10^3/3^3)-33(10^2/3^2)-4(10)+20

f(10/3)=6(10,000/81)+5(1,000/27)-33(100/9)-40+20

f(10/3)=2(10,000/27)+5,000/27-11(100/3)-20

f(10/3)=20,000/27+5,000/27-1,100/3-20

f(10/3)=[20,000+5,000-9(1,100)-27(20)]/27

f(10/3)=(20,000+5,000-9,900-540)/27

f(10/3)=14,560/27 different of 0, then x=10/3 is not a root of f(x)

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

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