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In-s [12.5K]
3 years ago
14

Write a polynomial f(x) that satisfies the given conditions.

Mathematics
1 answer:
patriot [66]3 years ago
6 0

Answer:

f(x) = (x-4)(x-\frac{1}{2})^2 = x^3-5x^2+4.25x -1

Step-by-step explanation:

Recall, if we have a polynomial of the form (x-a)^k \cdot (x-b)^m, then we say that a is a zero of multiplicity k and b is a zero of multiplicty m. For example, in the polynomial of the form (x+5)^10(x-2)^3 -5 is a zero of multiplicity 10 and 2 is a zero of multiplicity 3. If we want to know the degree of the polynomial,  just add the multiplicity of both zeros (13 in our example).

In this case, we know that the degree of our polynomial should be at least 3(multiplicity 2 and multiplicity 1). So, lets take the polynomial of the form

f(x)=(x-a)(x-b)^2).

In here, a is a zero with multiplicity 1 and b is a zero with multiplicity 2. We are also given that

f(0) = -1 = (0-a)(0-b)^2 = -a\codt b^2.

Which implies that 1 = a\cdot b^2. Since the square of any number is a positive number, it must happen that a>0. So, we have that

b= \pm \sqrt[]{\frac{1}{a}}.

We can choose any value of a and solve for b. Let us choose a=4. So we can have b=1/2 or b=-1/2. Let's use b=1/2. So our polynomial would be

f(x) = (x-4)(x-\frac{1}{2})^2 = x^3-5x^2+4.25x -1

which we can easily check that f(0)=-1.

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Natalija [7]

Answer:

  • 924/5 ft/s
  • 369.6 ft

Step-by-step explanation:

126 mi/h = (126 mi)/(1 h)·(5280 ft)/(1 mi)·(1 h)/(3600 s) = (126·5280/3600) ft/s

126 mi/h = 184.8 ft/s = 924/5 ft/s

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In 2 seconds, the parachutist falls ...

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4 0
3 years ago
14)If you multiply John's age by 4 and then
natulia [17]

Answer:

there was alot of math here but i got 10

Step-by-step explanation:

so first u add 10 and 2 u get 12 then u multiply 4 then u get 48 and divide that by 4 and then subtract 2 and get 10. hope this helped

6 0
3 years ago
Josh noticed, g, gallon of rain water collecting in a tank for, t, hours
STatiana [176]

Answer:

thr answer is C.

Step-by-step explanation:

because the time was already 3 hours and there were already 12 gallons of water

6 0
3 years ago
Find the interquartile range for a data set having the five-number summary: 3.5, 10.4, 16, 21.7, 27.7
vlabodo [156]

Answer: 17.75

Step-by-step explanation:

The interquartile range(IQR) is the 3rd quartile - the 1st quartile.

How to get quartiles:

First get the median:

3.5, 10.4, 16, 21.7, 27.7

10.4, 16, 21.7

16

Then find the median of the first half of data(3.5, 10.4)

(3.5+10.4)/2 = 6.95

Then find the median of the last half of data(21.7, 27.7)

(21.7+27.7)/2 = 24.7

Then to get the IQR subtract 6.95 from 24.7 to get 17.75

Hope it helps <3

5 0
3 years ago
What are these &lt; &gt; =???????????
madam [21]

These Are Less Than(<) and Greater Than(>) Symbols!!

Hope This Helps!!!

7 0
3 years ago
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