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LiRa [457]
3 years ago
10

According to the rational root theorem, what are all the potential rational roots of f(x)= 5x^3-7x+11

Mathematics
1 answer:
Tems11 [23]3 years ago
8 0

The rational root theorem states that the rational roots of a polynomial can only be in the form p/q, where p divides the constant term, and q divides the leading term.

In your case, both the leading term 5 and the constant term 11 are primes, so their only divisors are 1 and themselves.

So, the only feasible solutions are

\pm\dfrac{11}{5},\quad\pm 11,\quad \pm\dfrac{1}{5}, \pm 1

For the record, in this case, none of the feasible solutions are actually a root of the polynomial.

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Installment Buying TV Town sells a big screen smart HDTV for $600 down and monthly payments of $30 for the next 3 years. If the
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Answer:

(a). $1465.42

(b). $214.58

Step-by-step explanation:

We have been given that installment Buying TV Town sells a big screen smart HDTV for $600 down and monthly payments of $30 for the next 3 years. The interest rate is 1.25% per month on the unpaid balance.

(a) To find the cost of the TV, we will use monthly payment formula.

R=\frac{Pi}{1-(1+i)^{-n}}, where,

R = Periodic payment,

P = Loan amount,

i = Monthly interest rate in decimal form,

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n=3\times 12=36

1.25\%=\frac{1.25}{100}=0.0125

30=\frac{P*0.0125}{1-(1+0.0125)^{-36}}

30=\frac{0.0125P}{1-(1.0125)^{-36}}

30=\frac{0.0125P}{1-0.6394091578134724264}

30=\frac{0.0125P}{0.3605908421865275736}

10.817725265595827208=0.0125P

0.0125P=10.817725265595827208

P=\frac{10.817725265595827208}{0.0125}

P=865.41802124766617664

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We know that total cost of TV would be equal to down payment plus amount of loan that is:

865.42+600=1465.42

Therefore, the total cost of the TV would be $1465.42.

(b). First of all, we need to find total amount paid in 3 years by multiplying amount of each monthly payment by 36 (3 years equal to 36 months).

\$30\times 36=\$1080

To find the total amount of interest paid, we will subtract amount of loan from total payment.

\$1080-\$865.42=\$214.58

Therefore, the total amount paid in interest would be $214.58.

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