# If a polynomial function with rational coefficients has the zeros -1, 5, #-2+sqrt5#, what are the additional zeros?

Complex zeros and radical zeros always come in conjugate pairs:

The polynomial function is

By signing up, you agree to our Terms of Service and Privacy Policy

Given the zeros of the polynomial function are ( -1, 5, -2+\sqrt{5} ), the additional zeros can be found using the conjugate root theorem. This theorem states that if a polynomial has rational coefficients and ( a + bi ) is a root (where ( a ) and ( b ) are rational numbers and ( i ) is the imaginary unit), then its conjugate ( a - bi ) is also a root.

Since ( -2+\sqrt{5} ) is a root, its conjugate ( -2-\sqrt{5} ) must also be a root.

Therefore, the additional zeros of the polynomial function are ( -2-\sqrt{5} ) and any other complex conjugate pairs of the given zeros, if they exist.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the roots of #x^4-5x^2+4=0#?
- How do you combine like terms for #\sqrt { 16z } + 2\sqrt { 8z } - 3\sqrt { z }#?
- How do you find all the real and complex roots of #z^7+z^4+4z^3+4=0#?
- How do you find all the real and complex roots of #x^5 + 7*x^3 + 3*x + 2 = 0#?
- How do you find all the real and complex roots of #x^7 – x^5 + x^2 – 3x + 3 = 0#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7