Question

What is the use of a general form of a polynomial?Is thezero of a polynomial related with the coefficient of terms in the case of quadratic and cubic polynomial?

Answer 1

$$\begin{gathered} \mathrm{General}\mathrm{form}\mathrm{of}\mathrm{polynomial}\mathrm{is}\mathrm{used}\mathrm{for}\mathrm{the}\mathrm{easier}\mathrm{calculations}\mathrm{and}\mathrm{minimize}\mathrm{the}\mathrm{errors}. \\ \mathrm{If}\alpha \mathrm{and}\beta \mathrm{are}\mathrm{the}\mathrm{zeroes}\mathrm{of}\mathrm{the}\mathrm{quadratic}\mathrm{polynomial}a{x}^2+bx+c,\mathrm{then} \\ \alpha +\beta =\frac{-b}{a}\mathrm{and}\alpha \beta =\frac{c}{a} \\ \mathrm{And} \\ \mathrm{If}\alpha ,\beta \mathrm{and}\gamma \mathrm{are}\mathrm{the}\mathrm{zeroes}\mathrm{of}\mathrm{the}\mathrm{cubic}\mathrm{polynomial}a{x}^3+b{x}^2+cx+d,\mathrm{then} \\ \alpha +\beta +\gamma =\frac{-b}{a},\alpha \beta +\beta \gamma +\alpha \gamma =\frac{c}{a}\mathrm{and}\alpha \beta \gamma =\frac{-d}{a} \end{gathered}$$