Question

If the value of the polynomial x² $-$ mx + 7 is 35 when x = 2 then find m.

Answer 1

$$\begin{gathered} \mathrm{Let}p\left(x\right)=x^2-mx+7 \\ \mathrm{Then}p\left(2\right)=2^2-m\times 2+7 \\ =4-2m+7 \\ \therefore p\left(2\right)=-2m+11 \\ \mathrm{But}p\left(2\right)=35\left(\mathrm{Given}\right) \\ \mathrm{i}.\mathrm{e}.,-2m+11=35 \\ \Rightarrow -2m=35-11 \\ \Rightarrow -2m=24 \\ \therefore m=-12 \end{gathered}$$