Answer:
f(x) = x³ + 6x² + 13x + 10
Step-by-step explanation:
Note that complex roots occur in conjugate pairs, thus
x = - 2 + i is a root then x = - 2 - i is also a root
The roots are x = - 2, x = - 2 + i, x = - 2 - i, then the factors are
(x + 2), (x - (- 2 + i)) , (x - (- 2 - i)), that is
(x + 2), (x + 2 - i)(x + 2 + i)
The polynomial is the product of the factors
f(x) = (x + 2)(x + 2 - i)(x + 2 + i) ← expanding
= (x + 2)(x² + 2x + xi + 2x + 4 + 2i - xi - 2i - i²) → i² = - 1
= (x + 2)(x² + 4x + 4 + 1)
= (x + 2)(x² + 4x + 5) ← distribute
= x³ + 4x² + 5x + 2x² + 8x + 10 ← collect like terms
= x³ + 6x² + 13x + 10
Answer:
can you attach a picture
Step-by-step explanation:
I took the liberty of finding for the complete question.
And here I believe that the problem asks for the half life of Curium. Assuming
that the radioactive decay of Curium is of 1st order, therefore the
rate equation is in the form of:
A = Ao e^(-kt)
where,
A = amount after t years = 2755
Ao = initial amount = 3312
k = rate constant
t = number of years passed = 6
Therefore the rate constant is:
2755/3312 = e^(-6k)
-6k = ln (2755/3312)
k = 0.0307/yr
The half life, t’, can be calculated using the formula:
t’ = ln 2 / k
Substituting the value of k:
t’ = ln 2 / 0.0307
t’ = 22.586 years
or
t’ = 22.6 years
ANSWER
correct to 3 decimal places is 
EXPLANATION
We start counting from the first number after the decimal point.
So starting from 2, we count 3 decimal places to the right and land on 4.
Next, we check to see if the number after 4, is greater or equal 5, then we round up, else we round down.
Since that number is 5, it is greater than or equal to 5.
Therefore we round up to obtain
