Question

When examining the graph of a cubic polynomial function, how can you determine if all of the zeros are real?

Answer 1

Consider, the Cubic polynomial :

f(x)=
`ax^3 + b x^2 + c x +d`

Draw , the graph of cubic polynomial on two dimensional coordinate plane, and find number of times it cuts the x axis.The point where it cuts the x axis,are the roots of the cubic polynomial function or number of real roots that a cubic polynomial function possess is number of times it cuts the x axis.

Keep in mind, Imaginary root occur in pairs.

So, a cubic polynomial function has all real root , a single real root or no real root.

So, if graph cuts the x axis at three points (Either same or different) , showing the number of real roots possessed by the cubic polynomial function.