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Ivenika [448]
3 years ago
11

Use the Rational Root Theorem to list all possible rational roots for the equation.

Mathematics
2 answers:
Anna71 [15]3 years ago
8 0
Q^n + k^(n-1).... + P = 0
Like: 3x^3+9x-6=0

All rational roots will be rational factors of P/Q such that:

Q = 3 Factors: 1,3
P = -6 Factors: [+/-] 1,2,3,6

Possible Rational Roots: [1/1,1/3,2/1,2/3,3/1,3/3,6/1,6/3] = [+/-] 1,1/3,2,2/3,3,6

Now you just test them in the equation itself and where the input makes the function equal 0, you have a root.

For this polynomial, no roots are rational, so when you test it you'll find that it must only contain irrational roots and may only be solved by other means.
Mariana [72]3 years ago
6 0

\bf \stackrel{q}{3}x^3+9x-\stackrel{p}{6}~\hspace{5em}\stackrel{\textit{factors of \boxed{p}}}{3,2,1,6}\qquad \stackrel{\textit{factors of \boxed{q}}}{3,1}\qquad \qquad \pm\cfrac{p}{q} \\\\\\ \textit{therefore, using the \underline{rational root test}}


\bf \begin{cases} \pm \cfrac{3}{3}\implies &\pm 1\\\\ \pm \cfrac{3}{1}\implies &\pm 3\\\\ \end{cases}\quad \begin{cases} \pm \cfrac{2}{3}\\\\ \pm \cfrac{2}{1}\implies \pm 2 \end{cases}\quad \begin{cases} \pm \cfrac{1}{3}\\\\ \pm \cfrac{1}{1}\implies \pm 1 \end{cases}\quad \begin{cases} \pm \cfrac{6}{3}\implies &\pm 2\\\\ \pm \cfrac{6}{1}\implies &\pm 6 \end{cases}

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tatuchka [14]

' n '    the 'n'th term

1               4
2               2 
3               0
4              -2 .

In general, the 'n'th term of the sequence is   A(n) = 6 - 2n  .
3 0
3 years ago
Jim drove 204 miles in 4 hours. If he can keep the same pace how long will it take him to drive 918 miles
SSSSS [86.1K]
18 hours.

Proportions and stuff.

\frac{204}{4} = \frac{918}{x}

Cross multiply,

204x = 918 * 4

204x = 3672
/204      /204
x = 18

18 hours.
6 0
3 years ago
$3000 is invested at 3% annual interest for 3 years.<br> a. Simple Interest b. Compound Interest
stich3 [128]

Answer:

a. $270

b. $3,278.18

Step-by-step explanation:

Given that

The principal amount is $3,000

Annual rate of interest is 3%

And, the time period is  3 years

We need to find out the simple interest & compound interest

The following formulas should be used

a. For simple interest

= Principal × rate of interest × time period

= $3,000 × 3% × 3 years

= $270

b. For compound interest

= Principal × (1 + rate of interest)^time period

= $3,000 × (1 + 0.03)3

= $3,000 × 1.03^3

= $3,278.18

8 0
2 years ago
Select the term that best describes the statement A triangle is acute provided all the angles have a measure of less than 90 deg
Aloiza [94]
I think the correct answer is conjunction...
4 0
3 years ago
Read 2 more answers
Kevin wants to change the engine in her car. The current engine is 250 cubic centimeters and has a 14 inch fan belt. The new eng
Simora [160]

Option A) 14/250 = N/350 is correct.

Kevin wants to change the engine in her car. The current engine is 250 cubic centimeters and has a 14 inch fan belt. The new engine is 350 cubic centimeters and has proportionally larger fan belt.

<h3>What is proportionality?</h3>

proportionality can be defined as, how much the number is relatable to other number i.e. x =2y x is two times proportion to y.

Hence, in the question
for 250 cc engine it has 14 inch belt
for 350 cc engine it has N inch belt(let)
proportionality can be given as
14 ∝ 250
N ∝ 350
dividing both equation
N/14=350/250
or 14/250=N/350

Thus, the required proportion is given as 14/250=N/350.

Learn more about proportionality here:
brainly.com/question/8598338

#SPJ2

5 0
1 year ago
Read 2 more answers
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