which function below if either has zeros that are complex conjugates?
P(x)=x^4-7x^3-27x^2+63x+81
H(x)=x^4-x^2+25x-25
HElp!!!!!!!!!!!!!!!Asap
The school subject is math, not "HELP...."
If you want help, you need to follow directions. You also need to let the math teachers know what you do and don't understand so far.
I need that question please
To determine if a function has complex conjugate zeros, we need to analyze its coefficients. Complex conjugate zeros occur when a polynomial function has complex numbers as its zeros in conjugate pairs, i.e., if a + bi is a zero, then a - bi is also a zero.
Let's start with the first function P(x) = x^4 - 7x^3 - 27x^2 + 63x + 81:
The coefficients of this function are:
a = 1
b = -7
c = -27
d = 63
e = 81
Next, we need to check if any of the coefficients are non-zero:
- The constant term (e = 81) is non-zero.
Since the constant term is non-zero, we cannot guarantee that the function P(x) has complex conjugate zeros.
Now let's analyze the second function H(x) = x^4 - x^2 + 25x - 25:
The coefficients of this function are:
a = 1
b = 0
c = -1
d = 25
e = -25
Again, we need to check if any of the coefficients are non-zero:
- The constant term (e = -25) is non-zero.
Since the constant term is non-zero, we cannot guarantee that the function H(x) has complex conjugate zeros either.
To summarize, neither of the functions P(x) or H(x) have zeros that are complex conjugates.