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:
Step-by-step explanation:
so there is 32 kids....1/2 are blonde, 1/4 have black hair, 1/4 have brown hair
1/2(32) = 32/2 = 16 are blonde
1/4(32) = 32/4 = 8 have black hair
1/4(32) = 32/4 = 8 have brown hair
Answer:
Step-by-step explanation:
Answer:2516 pounds
Step-by-step explanation:
find the difference in gallons and the difference in the weights
46 - 14 = 32 gallons
2399 - 2191 = 208 pounds
so 32 gallons of gas weighs 208 pounds
find weight per pound: 208 pounds / 32 gallons = 6.5 pounds per gallon
round to 6.5 pounds per gallon
64 gallons - 46 gallons = 18 gallons
18 gallons x 6.5 pounds per gallon = 117 pounds
2399 + 117 = 2516 weight of plane with 64 gallons
