The perfect squares on either side of 21 are 16 and 25 of which the roots are:
4 and 5
Answer:
1. Fill in the box with 1
2. Fill in the box with -2
Step-by-step explanation:
Expression:
![(-2x^3 + [\ ]x)(x^{[\ ]}+1.5) = A](https://tex.z-dn.net/?f=%28-2x%5E3%20%2B%20%5B%5C%20%5Dx%29%28x%5E%7B%5B%5C%20%5D%7D%2B1.5%29%20%3D%20A)
Solving (1): Fill in the box to make it a polynomial.
To make it a polynomial, we simply fill in the box with a positive integer (say 1)
Fill in the box with 1
![(-2x^3 + [1]x)(x^{[1]}+1.5) = A](https://tex.z-dn.net/?f=%28-2x%5E3%20%2B%20%5B1%5Dx%29%28x%5E%7B%5B1%5D%7D%2B1.5%29%20%3D%20A)
Remove the square brackets


Open bracket

Reorder

The above expression is a polynomial.
This will work for any positive integer filled in the box
Solving (2): Fill in the box to make it not a polynomial.
The powers of a polynomial are greater than or equal to 0.
So, when the boxes are filled with a negative integer (say -2), the expression will cease to be a polynomial
Fill in the box with -2
![(-2x^3 + [-2]x)(x^{[-2]}+1.5) = A](https://tex.z-dn.net/?f=%28-2x%5E3%20%2B%20%5B-2%5Dx%29%28x%5E%7B%5B-2%5D%7D%2B1.5%29%20%3D%20A)
Remove the square brackets

Reorder

Open brackets

Collect Like Terms


Notice that the least power of x is -1.
Hence, this is not a polynomial.
Answer:
- boat: 16 mph
- current: 4 mph
Step-by-step explanation:
speed = distance / time
The rate downriver is (60 mi)/(3 h) = 20 mi/h.
The rate upriver is (60 mi)/(5 h) = 12 mi/h.
The rate of the boat in still water is the average of these:
(20 +12)/2 mi/h = 16 mi/h
The rate of the current is the difference between the boat speed and actual speed:
16 mi/h - 12 mi/h = 4 mi/h
Answer:
c
Step-by-step explanation:
c
Answer:
x can have two complex solutions, which are:
-2 + i
-2 - i
Step-by-step explanation:
2x² + 8x + 10 = 0
4x² + 16x + 20 = 0
4x² + 16x + 16 = -4
(2x + 4)² = -4
2x + 4 = √-4
2x = -4 ± i√4
2x = -4 ± 2i
x = -2 ± i
So x is equal to -2 + i and -2 - i.