Question

Which of the following is true
A polynomial of degree 4 has 4 unique zeros
A polynomial of degree 5 has at least 1 real zero
A polynomial of degree 2 has at least 1 real zero
Please show work and explain to me how each works

Answer 1

As stated previously, complex roots come in pairs so a degree five will have at least one real zero. You can also use the MVT to show the existence of a zero.

Answer 2

ok but what aobut for the others

Answer 3

they are explained in your other post of the same question

Answer 4

The left end behavior of a polynomial of odd degree is the opposite of the right end behavior: gots to cross the x-axis, and that's a real zero.