How to get x when x^3-x^2+x-1=0?
1 answer:
Answer:
x = 1 or x = ± i
Step-by-step explanation:
Note the sum of the coefficients
1 - 1 + 1 - 1 = 0
This indicates that x = 1 is a root, thus (x - 1) is a factor
Using long division or synthetic division, then
x³ - x² + x - 1 = (x - 1)(x² + 1), thus
(x - 1)(x² + 1) = 0
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x² + 1 = 0 ⇒ x² = - 1 ⇒ x = ± = ± i
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Answer:
482 km
63.94 degrees
Step-by-step explanation:
to solve this question we will use the cosine rule. For starters, draw your diagram. From point A, up north is 500km and 060 from there, another 300. If you join the point from the road junction back to the starting point, yoou have a triangle.
Cosine rule states that
C =
where both A and B are the given distances, 500 and 300 respectively, C is the 3rd distance we're looking for and c is the given angle, 060
solving now, we have
C =
C =
C =
C =
C =
C = 482 km
The bearing can be gotten by using the Sine Rule.
=
sina/500 = sin60/482
482 sina = 500 sin60
sina =
sina = 0.8983
a = sin^-1(0.8983)
a = 63.94 degrees