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AleksandrR [38]
3 years ago
6

Form a polynomial f(x) with real coefficients having the given degree and zeros.

Mathematics
1 answer:
dimaraw [331]3 years ago
6 0
There are many polynomials that fit the bill,
f(x)=a(x-r1)(x-r2)(x-r3)(x-r4)  where a is any real number not equal to zero.
A simple one is when a=1.
where r1,r2,r3,r4 are the roots of the 4th degree polynomial.
Also note that for a polynomial with *real* coefficients, complex roots *always* come in conjugages, i.e. in the form a±bi  [±=+/-]

So a polynomial would be:
f(x)=(x-(-4-5i))(x-(-4+5i))(x--2)(x--2)
or, simplifying
f(x)=(x+4+5i)(x+4-5i)(x+2)^2
=x^4+12x^3+77x^2+196x+164   [if you decide to expand]
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The sum of a number and its square is 182. Find the number.
Mars2501 [29]

Answer:

13 and -14 satisfy this condition

Step-by-step explanation:

Let's represent that number as x

and the square of x is x^2

So,

x + x^2 = 182

Subtract 182 from both sides

x + x^2 - 182 = 182 - 182

x + x^2 - 182 = 0

rearrange the quadratic equation

x^2 + x -182 = 0

let's use the quadratic formula

\frac{-b+\sqrt{b^2-4ac} }{2a}       or      \frac{-b-\sqrt{b^2-4ac} }{2a}

a = 1, b = 1, c = -182

\frac{-1+\sqrt{1^2-4*1*(-182)} }{2*1}       or     \frac{-1-\sqrt{1^2-4*1*(-182)} }{2*1}

\frac{-1+\sqrt{1+728} }{2}      or         \frac{-1-\sqrt{1+728} }{2}

\frac{-1+\sqrt{729} }{2}            or    \frac{-1-\sqrt{729} }{2}

\frac{-1+{27} }{2}     or    \frac{-1-{27} }{2}

\frac{26}{2}     or    \frac{-28}{2}

13 or    - 14

Lets check

13 + 13^2 = 13 + 169

= 182

Also,

-14 + (-14^2) = -14 + 196

= 182

8 0
3 years ago
A boat sails for 5 hours at 30 mph in a direction 164°56'. How far south has it sailed (to the nearest mile)?
Valentin [98]
Total distance covered = 5 x 30 = 150 miles
Angle of travel with respect to south pole = 180 - 164°56' = 15°4'

Let the distance southwards covered be x, then
cos 15°4' = x/150
Thus, x = 150 cos 15°4' = 144.84

Therefore, the distance covered southwards = 145 miles to the nearest mile.
5 0
3 years ago
What are the domain and range of the function of the graph
alexira [117]
The domain is the x intercept and the y intercept is the range
8 0
3 years ago
Read 2 more answers
Factor k 2 + 8k + 15.<br> answers.<br> (k + 1)(k + 15)<br> (k + 8)(k + 7)<br> (k + 3)(k + 5)
KATRIN_1 [288]
K^2 +3k +5k + 15
k (k+3) +5 (k+3)
(k+5)(k+3)


So, the correct option is the last one.
4 0
3 years ago
Cal is buying T-shirts and shorts. T-shirts cost $12 and shorts cost $25. He plans on spending no more than $160 and wants to bu
aksik [14]

Answer at least what, u you missed part of the question

Step-by-step explanation:

8 0
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