Answer:
8.15
Step-by-step explanation:
Answer:
![f(x)=x^5-6x^4+14x^3-24x^2+40x](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E5-6x%5E4%2B14x%5E3-24x%5E2%2B40x)
Step-by-step explanation:
<u>Given information</u>:
- Polynomial function with real coefficients.
- Zeros: 0, 2i and (3+i).
For any complex number
, the complex conjugate of the number is defined as
.
If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.
Therefore, if f(x) is a polynomial with real coefficients, and 2i is a root of f(x)=0, then its complex conjugate -2i is also a root of f(x)=0.
Similarly, if (3+i) is a root of f(x)=0, then its complex conjugate (3-i) is also a root of f(x)=0.
Therefore, the polynomial in factored form is:
![f(x)=ax(x-2i)(x-(-2i))(x-(3+i))(x-(3-i))](https://tex.z-dn.net/?f=f%28x%29%3Dax%28x-2i%29%28x-%28-2i%29%29%28x-%283%2Bi%29%29%28x-%283-i%29%29)
![f(x)=ax(x-2i)(x+2i)(x-3-i)(x-3+i)](https://tex.z-dn.net/?f=f%28x%29%3Dax%28x-2i%29%28x%2B2i%29%28x-3-i%29%28x-3%2Bi%29)
As we have not been given a leading coefficient, assume a = 1:
![f(x)=x(x-2i)(x+2i)(x-3-i)(x-3+i)](https://tex.z-dn.net/?f=f%28x%29%3Dx%28x-2i%29%28x%2B2i%29%28x-3-i%29%28x-3%2Bi%29)
Expand the polynomial:
![f(x)=x(x^2+2ix-2ix-4i^2)(x^2-3x+xi-3x+9-3i-xi+3i-i^2)](https://tex.z-dn.net/?f=f%28x%29%3Dx%28x%5E2%2B2ix-2ix-4i%5E2%29%28x%5E2-3x%2Bxi-3x%2B9-3i-xi%2B3i-i%5E2%29)
![f(x)=x(x^2-4i^2)(x^2-6x+9-i^2)](https://tex.z-dn.net/?f=f%28x%29%3Dx%28x%5E2-4i%5E2%29%28x%5E2-6x%2B9-i%5E2%29)
![f(x)=x(x^2-4(-1))(x^2-6x+9-(-1))](https://tex.z-dn.net/?f=f%28x%29%3Dx%28x%5E2-4%28-1%29%29%28x%5E2-6x%2B9-%28-1%29%29)
![f(x)=x(x^2+4)(x^2-6x+10)](https://tex.z-dn.net/?f=f%28x%29%3Dx%28x%5E2%2B4%29%28x%5E2-6x%2B10%29)
![f(x)=(x^3+4x)(x^2-6x+10)](https://tex.z-dn.net/?f=f%28x%29%3D%28x%5E3%2B4x%29%28x%5E2-6x%2B10%29)
![f(x)=x^5-6x^4+10x^3+4x^3-24x^2+40x](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E5-6x%5E4%2B10x%5E3%2B4x%5E3-24x%5E2%2B40x)
![f(x)=x^5-6x^4+14x^3-24x^2+40x](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E5-6x%5E4%2B14x%5E3-24x%5E2%2B40x)
First, put fill in the X's with 2.
y = 2*2*3 - 6*2
Next, multiply.
y = 12 - 12
Finally, subtract!
y = 0
Apparently, Y equals 0.
Step-by-step explanation:
Hi Friend !!!
Here is ur answer !!!
(x-1)(x+1)(x²+1)(x^4 + 1)
= (x²-1)(x²+1)(x^4 + 1)
=( x^4 -1)(x^4 + 1)
=( x^8 -1)
The whole is with the help of (a-b) (a+b) = a²-b²
Hope it helps u :-)
Answer:
1.5 kg
Step-by-step explanation:
Assuming it scales linearly: the higher tin holds 9/6 as many biscuits, so:
9/6 · 1 kg = 1.5 kg