Fifth degree polynomial; scary stuff. We know it has five complex roots, counting multiplicities. How many are real?
The rational root test tells us we only have to try the divisors of 9, so 1, -1, 3, -3, 9, -9. We find x=3 gives
243 - 243 - 54 + 54 - 9 + 9 = 0
in nice pairs.
So x-3 is a factor and we can divide to get a 4th degree polynomial. The division is a bit easier than usual.
x^4 - 2x^2 - 3
x - 3 | x^5 - 3x^4 - 2x^3 + 6x^2 - 3x + 9
x^5 - 3x^4
0 - 2x^3 + 6x^2
0 - 3x + 9
0
So we get
It's downhill from here. The new factor is really just a quadratic in x squared, and factors easily:
And now if we descend into irrational and complex numbers, we can further factor
and we can read off our roots,
We have one rational root, namely 3, and two irrational roots, the square roots of three, and two purely imaginary roots.
Answer: 1 rational, 2 irrational
Answer:
One rational and 2 irrational zeroes
Step-by-step explanation:
I agree with the other guy.
f(3) = 0 so x = 3 is a rational root.
There also are 2 irrational roots and 2 complex roots.
.
.
Naya has $60. Each box of cupcakes costs $12.
60÷12=5
Naya can buy 5 boxes of cupcakes.
undetectable) in 20 hours. There
exists a set of ordered pairs (t, m),
where t is the amount of time in hours
that the substance has been decaying,
and m is the mass in grams that has
decayed.
If t > 0, what is the range of m?
Answer:
The range is 0 < m < 2000 when t > 0
Step-by-step explanation:
* Lets explain how to solve the problem
- The exponential function is , where
a is the initial amount and b is the growth factor
- If b > 1, then it is exponential growth function
- If 0 < b < 1, then it is exponential decay function
* Lets solve the problem
- A 2000 gram sample of radioactive matter will completely decay
(be undetectable) in 20 hours
- There is a set of ordered pairs (t , m) exists, where t is the amount
of time in hours that the substance has been decaying and m is
the mass in grams that has decayed
∵ We can represent this situation by an exponential decay function
∴ , where b is the growth factor which is
greater than zero and less than 1 , t is the lime in hours and
m(t) is the mass of the substance in gram
- In any function the domain is the value of x and the range is
the value of y
∵ In the function the domain is t and the range is m
∵ When t = 0 then m = 2000 ⇒ initial amount
∵ When t = 20 then m will be closed to zero
∴ The domain of the function is 0 < t < 20
∴ The range of the function is 0 < m < 2000
* The range is 0 < m < 2000 when t > 0
Answer:
y=13
Step-by-step explanation:
15+y=28=28-15=13
your welcome!