# Thread: Zeros of a function

1. ## Zeros of a function

Okay, I fully understand that complex zeros exist in conjugate pairs, but what about irrational zeros; it would appear as though this would apply to them as well. Am I mistaken?

Also, how do you find the coefficients of of the leading terms of a rational function? Would I substitute an x and y value in and solve in the form of: y=a_1(x-b)/a_2(x-c), where b and c are the constants, and a_1 and a_2 are the leading coefficients, which I would solve individually?

Thank you

2. ## Re: Zeros of a function

Originally Posted by Bashyboy
Okay, I fully understand that complex zeros exist in conjugate pairs, but what about irrational zeros; it would appear as though this would apply to them as well. Am I mistaken?

for your 1st question ...Math Forum - Ask Dr. Math

Also, how do you find the coefficients of of the leading terms of a rational function? Would I substitute an x and y value in and solve in the form of: y=a_1(x-b)/a_2(x-c), where b and c are the constants, and a_1 and a_2 are the leading coefficients, which I would solve individually?
... can you provide a specific example of what you're looking for in your second question?

3. ## Re: Zeros of a function

For a polynomial with integer coefficients, the irrational zeros do not have to occur in conjugate pairs. If there are exactly two irrational zeros, they will be a conjugate pair.