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BabaBlast [244]
3 years ago
9

write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the zeros 2, -3, a

nd -3i
Mathematics
1 answer:
AysviL [449]3 years ago
5 0

Answer:

Do you have some examples?

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Find the first three terms in the expansion , in ascending power of x , of (2+x)^6 and obtain the coefficient of x^2 in the expa
Nataly_w [17]

Answer:

The first 3 terms in the expansion of (2 + x)^{6} , in ascending power of x are,

64 , 192 \times x^{1} {\textrm{  and  }}240 \times x^{2}

coefficient of x^{2} in the expansion of (2+x - x^{2})^{6} = (240 - 192) = 48

Step-by-step explanation:

(2+x)^{6}

= \sum_{k=0}^{6}(6_{C_{k}} \times x^{k} \times 2^{6 - k})

= 6_{C_{0}} \times x^{0} \times 2^{6}  + 6_{C_{1}} \times x^{1} \times 2^{5} + 6_{C_{2}} \times x^{2} \times 2^{4} + terms involving higher powers of x

= 64 + 192 \times x^{1} + 240 \times x^{2} + terms involving higher powers of x

so, the first 3 terms in the expansion of (2 + x)^{6} , in ascending power of x are,

64 , 192 \times x^{1} {\textrm{  and  }}240 \times x^{2}

Again,

(2+x - x^{2})^{6}

= \sum_{k=0}^{6}(6_{C_{k}} \times (2 + x)^{k} \times (-x^{2})^{6 - k})

Now, by inspection,

the term x^{2} comes from k =5 and k = 6

for k = 5, the coefficient of  x^{2}  is , (-32) \times 6 = -192

for k = 6 , the coefficient of x^{2} is, 6_{C_{2}} \times 2^{4} = 240

so,   coefficient of x^{2} in the final expression = (240 - 192) = 48

3 0
3 years ago
What angles go with the angle pairs? Just a simple checklist please :).​
Anni [7]

Answer:

Here is the answer

Step-by-step explanation:

∠1 and ∠6 are adjacent because they share the same vertex and the same common side.

∠2 and ∠5 are vertical angles since they have pairs on opposite sides of the angle.

∠3 and ∠6 have none of the above.

∠5 and ∠3 are a linear pair because the angles are opposite of each other.

8 0
3 years ago
A mountain gorilla weighs 135 pounds and is gaining pound each week. An eastern gorilla
Tju [1.3M]

Answer:

njnnnnnnn

Step-by-step explanation:

nmkm

6 0
3 years ago
A Playstation 5 gaming console is initially priced at $500 and the price rises such that the new price is $550. What is the perc
konstantin123 [22]

Answer:

10%

Step-by-step explanation:

raises $50 from $500 500/50= 10=10%

8 0
3 years ago
|c- 24| = 7c<br><br> :D :D :D
Ivanshal [37]

c\geq0\\\\\\ |c- 24| = 7c\\\\c-24=7c \vee c-24=-7c\\\\6c=-24 \vee -8c=-24\\\\c=-4 \vee c=3\\\\-4\not \geq0\\\\\boxed{c=3}

3 0
3 years ago
Read 2 more answers
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