What does the fundamental theorem of algebra tell us about a polynomial

The video tutorial covers the fundamental theorem of algebra, explaining how the degree of a polynomial indicates the number of zeros, both real and complex. It emphasizes that complex zeros occur in pairs due to the nature of square roots of negative numbers. The tutorial also compares rational and irrational zeros, highlighting the necessity of having both positive and negative counterparts for irrational zeros.

What does the fundamental theorem of algebra tell us about a polynomial?

• The number of real zeros it has

• The number of complex zeros it has

• The degree of the polynomial

• The total number of zeros, both real and complex

Why is it impossible to have an odd number of complex zeros?

• Complex zeros are always real

• Complex zeros come in pairs due to the square root of a negative number

• Complex zeros are imaginary

• Complex zeros are always positive

If a polynomial has a degree of 4, how many complex zeros can it have?

• Four

• One

• Three

• Two

What happens when you take the square root of a negative number?

• You get a zero

• You get a complex number with a plus or minus

• You get a real number

• You get a positive number

If the square root of 3 is an irrational zero, what else must be a zero?

• Square root of 3

• Three

• Negative square root of 3

• Zero