Answer:
x = -2, x = 3 − i√8, and x = 3 + i√8
Step-by-step explanation:
g(x) = x³ − 4x² − x + 22
This is a cubic equation, so it must have either 1 or 3 real roots.
Using rational root theorem, we can check if any of those real roots are rational. Possible rational roots are ±1, ±2, ±11, and ±22.
g(-1) = 18
g(1) = 18
g(-2) = 0
g(2) = 12
g(-11) = 1782
g(11) = 858
g(-22) = -12540
g(22) = 8712
We know -2 is a root. The other two roots are irrational. To find them, we must find the other factor of g(x). We can do this using long division, or we can factor using grouping.
g(x) = x³ − 4x² − 12x + 11x + 22
g(x) = x (x² − 4x − 12) + 11 (x + 2)
g(x) = x (x − 6) (x + 2) + 11 (x + 2)
g(x) = (x (x − 6) + 11) (x + 2)
g(x) = (x² − 6x + 11) (x + 2)
x² − 6x + 11 = 0
Quadratic formula:
x = [ 6 ± √(36 − 4(1)(11)) ] / 2
x = (6 ± 2i√8) / 2
x = 3 ± i√8
The three roots are x = -2, x = 3 − i√8, and x = 3 + i√8.
Answer:
a) when the slopes are equal
Step-by-step explanation:
The slopes of lines can be used to define the nature of lines.
Two parallel lines have equal slopes and the product of slopes of perpendicular lines is -1.
Hence, we can conclude that two distinct non-vertical lines parallel when
a) when the slopes are equal ..
So, option a is correct ..
Answer:
0.3125
Step-by-step explanation:
If it decreases by 50% each time it hits the ground then all you have to do is divide 10 by 2 (50%) each time it bounces.
10 / 2 = 5 (first bounce)
5 / 2 = 2.5 (second bounce)
2.5 / 2 = 1.25 (third bounce)
Ect. . .
Until on the fifth bounce it is 0.3125m high.