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

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

psymon · Answer

I would say the 2nd one, degree 5 has at leas 1 real zero. My reasoning is based on two things, the first of them being end behavior. The end behavior of a function that has an even degree goes in the same direction. Meaning you could start above the x-axis and never cross the x-axis:

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