Given a cubic polynomial function px ax2 bx2 cx d a b c

Given a cubic polynomial function p(x) = ax^2 + bx^2 + cx + d [a, b, c, d notequalto 0], answer the following questions. Justify each answer. How many x-intercepts can there be? Does the degree of this polynomial function any x-intercepts? Will the graph pass through the origin? Could the graph \'touch\' the x-axis in two different ? Identify the end behavior of the graph. If known that one zero m ml and another zero is Imaginary, what can be determined about the remaining zeros?

Solution

1)As it is a cubic polynomial there can be 3 x-intercepts

2)Here the degree of polynomial is 3 which implies that there are 3 x-intercepts

3)No,the graph doesn\'t passes through the origin as d is not equal to zero.

4)Yes,the graph can touch the x-axis in two different places.

5)If one zero is real and another zero is imaginary then the third zero must be imaginary which is conjugate of previous imaginary zero.