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butalik [34]
2 years ago
7

If 2i is a zero of f(x)=x^4+x^2+a, find the value of a

Mathematics
1 answer:
Sedbober [7]2 years ago
5 0

By the polynomial remainder theorem, because <em>x</em> = 2<em>i</em> is a zero of <em>f(x)</em>, we have no remainder upon dividing <em>f(x)</em> by <em>x</em> - 2<em>i</em>.

Computing the quotient yields

\dfrac{x^4+x^2+a}{x-2i} = x^3+2ix^2-3x-6i+\dfrac{12+a}{x-2i}

Then if the remainder term is 0, follows that <em>a</em> = -12.

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How did the first line get to the second line??? (Check Picture)
ddd [48]

Step-by-step explanation:

15( \frac{11\pi}{6} ) \\ 15 \div 3 = 5 \\ 6 \div 3 = 2 \\  = 5( \frac{11\pi}{2} )

11 \times 5 \\  =  \frac{55\pi}{2}

8 0
2 years ago
1) Justin wants to buy a new iPod that costs $250.
PtichkaEL [24]

30/100× 250 = 70

250 - 70 = 180

agree, he'll save up to $70 and get the ipod at price $180

5 0
2 years ago
Can someone please help me find the area of this polygon, thank you!
Amanda [17]

Answer:

<h2>270 ft²</h2>

Step-by-step explanation:

<h3>METHOD 1:</h3>

<em>Look at the picture</em>

We can divide a given polygon into three rectangles:

21ft\ \times\ 10ft,\ 4ft\ \times\ 6ft,\ 6ft\ \times\ 6ft

The formula of an area of a rectangle <em>l × w </em>:

A=l\cdot w

Calculate the area of ​​each of the rectangles:

A_1=(21)(10)=210\ ft^2\\\\A_2=(4)(6)=24\ ft^2\\\\A_3=(6)(6)=36\ ft^2

The area of the given polygon:

A=A_1+A_2+A_3\\\\A=210+24+36=270\ ft^2

<h3 /><h3>METHOD 2:</h3>

<em>Look at the second picture</em>.

We subtract the field of the smaller rectangle (<em>11ft × 6ft</em>) from the field of the large rectangle (<em>21ft × 16ft</em>):

A_S=(11)(6)=66\ ft^2\\\\A_L=(21)(16)=336\ ft^2\\\\A=A_L-A_S\to A=336-66=270\ ft^2

7 0
3 years ago
Really need help please help me please please
Maru [420]

Answer:

y = 3/4x + 3

Step-by-step explanation:

you should only have y in one side and everything in other side of the equation. so you will first have -4y = -3x -12 , then you'll have to divide the right part of the equation by -4 . then you will have y = 3/4x + 3

3 0
2 years ago
I need help asap!!!!!
ycow [4]
It equals to 2 because 3 times -4 is -12 and -12 divided by -6 is 2
5 0
2 years ago
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