Answer:
Step-by-step explanation:
<u>Given information</u>:
- Polynomial function with real coefficients.
- Zeros: 0, 2i and (3+i).
For any complex number 
, the complex conjugate of the number is defined as 
.
If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.
Therefore, if f(x) is a polynomial with real coefficients, and 2i is a root of f(x)=0, then its complex conjugate -2i is also a root of f(x)=0.
Similarly, if (3+i) is a root of f(x)=0, then its complex conjugate (3-i) is also a root of f(x)=0.
Therefore, the polynomial in factored form is:
As we have not been given a leading coefficient, assume a = 1:
Expand the polynomial:
If you are looking for g then the answer is g<34
The sum of any geometric sequence (if it converges, r^2<1) is of the form:
s(n)=a(1-r^n)/(1-r), a=initial term, r=common ratio, n=number of terms...
s(n)=30(1-0.4^n)/(0.6)
s(n)=50(1-0.4^n)
Since r<1 the sum of the infinite series is just:
s=50
The y's value is given in the first equation.
. Now to solve, we will, plug it's value in the second equation.
Now we have x's value, we will plug it's value in the first equation.(We can plug it in the second one too, but plugging it the first one will make it easier.)
(-4,-4)(1,3)
slope = (3 - (-4) / (1 - (-4)
slope = (3 + 4) / (1 + 4) = 7/5
y - y1 = m(x - x1)...using (-4,-4)
slope(m) = 7/5
y - (-4) = 7/5(x - (-4) =
y + 4 = 7/5(x + 4) <==here is one
y - y1 = m(x - x1)..using (1,3)
slope = 7/5
y - 3 = 7/5(x - 1) <== here is the other one
