Question

There at most how many zeroes possible for any cubic polynomial?

Answer 1

Consider the cubic polynomial
$$\begin{gathered} a{x}^3+b{x}^2+cx+d. \\ \mathrm{Since}\mathrm{the}\mathrm{above}\mathrm{polynomial}\mathrm{is}\mathrm{of}\mathrm{degree}3,\mathrm{so}\mathrm{it}\mathrm{can}\mathrm{not}\mathrm{have}\mathrm{more}\mathrm{than}3\mathrm{zeroes}. \\ \mathrm{Hence}\mathrm{a}\mathrm{cubic}\mathrm{polynomial}\mathrm{has}\mathrm{atmost}3\mathrm{zeroes}. \end{gathered}$$