Answer:
Hope this helps:
FG=17
Step-by-step explanation:
X+11=3X+1
11=2X+1
12=2X
X=6
(6)X+11=17=FG
Answer:
How many friends?
Step-by-step explanation:
The answer is the absolute value of -13 is thirteen and the absolute value of 15 is 15 so I-13I<I15I
Simplest polynomial function is ![x^4-x^3-11x^2+9x+18.](https://tex.z-dn.net/?f=x%5E4-x%5E3-11x%5E2%2B9x%2B18.)
Solution:
Given data:
Zeroes are 3i, –1, 2.
3i is a complex root of the function.
If 3i is a zero of the polynomial then –3i is also a zero of the polynomial.
Therefore zeroes are 3i, –3i –1, 2.
By factor theorem,
If a is zero of the function, then (x – a) is a factor of the polynomial.
So, the factors are (x – 3i), (x + 3i), (x + 1), (x –2).
On multiplying the factors, we get the polynomial.
![(x - 3i) (x + 3i) (x + 1) (x -2)](https://tex.z-dn.net/?f=%28x%20-%203i%29%20%28x%20%2B%203i%29%20%28x%20%2B%201%29%20%28x%20-2%29)
![=(x^2+3ix-3ix+(3i)^2)(x^2-2x+x-2)](https://tex.z-dn.net/?f=%3D%28x%5E2%2B3ix-3ix%2B%283i%29%5E2%29%28x%5E2-2x%2Bx-2%29)
![=(x^2-9)(x^2-x-2)](https://tex.z-dn.net/?f=%3D%28x%5E2-9%29%28x%5E2-x-2%29)
Since the value of ![i^2=-1](https://tex.z-dn.net/?f=i%5E2%3D-1)
![=x^2(x^2-x-2)-9(x^2-x-2)](https://tex.z-dn.net/?f=%3Dx%5E2%28x%5E2-x-2%29-9%28x%5E2-x-2%29)
![=x^4-x^3-2x^2-9x^2+9x+18](https://tex.z-dn.net/?f=%3Dx%5E4-x%5E3-2x%5E2-9x%5E2%2B9x%2B18)
![=x^4-x^3-11x^2+9x+18](https://tex.z-dn.net/?f=%3Dx%5E4-x%5E3-11x%5E2%2B9x%2B18)
Simplest polynomial function is ![x^4-x^3-11x^2+9x+18.](https://tex.z-dn.net/?f=x%5E4-x%5E3-11x%5E2%2B9x%2B18.)