Thread: Zeros

Please clarify this for me.

1. Whatever the degree of the polynomial is, it is the total number of zeros. (real and complex) Is this statement correct?
2. Does "distinct zeros" mean "real zeros" It is the same thing?
3. For this polynomial f(x) = x^2 (x-3)^3 (x+2)^2 , there are three real zeros, does it mean that it has four complex zeros?
4. will you please graph f(x) = x^2 (x-3)^3 (x+2)^2

thank you

Originally Posted by oceanmd

Please clarify this for me.

1. Whatever the degree of the polynomial is, it is the total number of zeros. (real and complex) Is this statement correct?

No and yes, consider the polynomial x^2+2x+1, this has a single root but
is of degree 2. However if we count the mutiple root twice then we have
two roots.

So if we count the multiplicities of the roots this is true.

RonL

Originally Posted by oceanmd

2. Does "distinct zeros" mean "real zeros" It is the same thing?

No distinct zeros does not mean real zeros, you may have distinct comples zeros. Eample x^2-2x-2 has two distinct non-real zeros.

RonL

Originally Posted by oceanmd

3. For this polynomial f(x) = x^2 (x-3)^3 (x+2)^2 , there are three real zeros, does it mean that it has four complex zeros?

No all the roots are real but have multiplicities 2,3 and 2 respectivly.

RonL