State the possible number of imaginary zeros of g(x)= x^4+3x^3+7x^2-6x-13
this is how far Ive gotten:there are 4 zeros,3 positive and 1 negative
If you've found four real zeroes, then there are no imaginary zeroes. You can also see that there are no imaginary zeroes directly:
Put x = i y in the equation:
y^4 - 3iy^3 - 7y^2- 6iy - 13 = 0
Equate real and imaginary parts to zero:
y^4 - 7 y^2 - 13 = 0
And:
y^3 + 2 y = 0
The last equation has only one solution:
y = 0
But this does not satisfy the first equation.
so what is the answer? my choices are A)3 or 1
B)2,4,0
c)exactly 1
d)exactly 3
is it B?
Yes, the answer is B
I think it's B. Good luck!
Yes, the answer is B) 2, 4, 0.
To find the possible number of imaginary zeros, you need to determine the number of non-real or complex zeros.
In the given polynomial function g(x) = x^4 + 3x^3 + 7x^2 - 6x - 13, you have already determined that there are 4 zeros, 3 positive and 1 negative. However, this information pertains to the real zeros of the function.
To find the complex zeros, you can use the Fundamental Theorem of Algebra, which states that a polynomial of degree n will have exactly n complex zeros, including repeated zeros. Since the degree of the given function is 4, it can have at most 4 complex zeros.
Since you have already found 4 real zeros, you can conclude that there are no imaginary zeros. Therefore, the correct answer is B) 2, 4, 0, indicating that there are 2 complex zeros and 0 imaginary zeros.