Question

State true or false
a. Zero of polynomial is always zero
b.The degree of the sum of two polynomials each of degree 5 is always 5

Answer 1

Dear student
$$\begin{gathered} \mathrm{a})\mathrm{False}. \\ \mathrm{Consider}{\mathrm{x}}^2-4=0 \\ \Rightarrow {\mathrm{x}}^2=4 \\ \Rightarrow \mathrm{x}=\pm 2 \\ \mathrm{So},\mathrm{here}\mathrm{zeros}\mathrm{are}\pm 2 \\ \mathrm{b})\mathrm{True} \\ \mathrm{The}\mathrm{degree}\mathrm{of}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{two}\mathrm{polynomials}\mathrm{each}\mathrm{of}\mathrm{degree}5\mathrm{is}\mathrm{always}5.\mathrm{While}\mathrm{addition}\mathrm{or}\mathrm{subtraction} \\ \mathrm{coefficients}\mathrm{are}\mathrm{added}\mathrm{and}\mathrm{power}\mathrm{of}\mathrm{variables}\mathrm{are}\mathrm{not}\mathrm{affected}. \end{gathered}$$
Regards