A third-degree polynomial has 4 intercepts.
A third-degree function can have as many as 3 zeros only

true or false for both

Question

A third-degree polynomial has 4 intercepts. 
A third-degree function can have as many as 3 zeros only

true or false for both

mertsj · Answer

False
True

anonymous · Answer

explanation?

anonymous · Answer

@Mertsj

mertsj · Answer

A third degree polynomial might be (x+1)(x-2)(x+3)=0
That would have three roots, that is 3 x intercepts.

mertsj · Answer

If you have another root, there would be another factor and hence it would be a 4th degree polynomial.

mertsj · Answer

In the following, p will be used to represent the polynomial, so we have

    p = a_0 + a_1 x + .... + a_n x^n. 

A root of the polynomial p is a solution of the equation p = 0, that is a  number a such that p(a) = 0.

The fundamental theorem of algebra combined with the factor theorem states that the polynomial p has n roots, if they are counted with their multiplicities.