Question

Find the zero of the polynomial in each of the following:

(i) p(x) = x + 2
(ii) q(x) = 4x $-$ 12
(iii) r(x) = 5 $-$ 6x
(iv) p(y) = y + 1
(v) p(m) = m
(vi) q(y) = 4y

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\mathrm{To}\mathrm{find}\mathrm{the}\mathrm{zero}\mathrm{of}p\left(x\right),\mathrm{we}\mathrm{will}\mathrm{solve}\mathrm{the}\mathrm{equation}p\left(x\right)=0. \\ \mathrm{We}\mathrm{have}x+2=0 \\ \Rightarrow x=-2 \\ \therefore -2\mathrm{is}\mathrm{the}\mathrm{zero}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{polynomial}. \end{gathered}$$

$$\begin{gathered} \left(\mathrm{ii}\right)\mathrm{To}\mathrm{find}\mathrm{the}\mathrm{zero}\mathrm{of}q\left(x\right),\mathrm{we}\mathrm{will}\mathrm{solve}\mathrm{the}\mathrm{equation}q\left(x\right)=0. \\ \mathrm{We}\mathrm{have}4x-12=0 \\ \Rightarrow 4x=12 \\ \Rightarrow x=3 \\ \therefore 3\mathrm{is}\mathrm{the}\mathrm{zero}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{polynomial}. \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iii}\right)\mathrm{To}\mathrm{find}\mathrm{the}\mathrm{zero}\mathrm{of}r\left(x\right),\mathrm{we}\mathrm{will}\mathrm{solve}\mathrm{the}\mathrm{equation}r\left(x\right)=0. \\ \mathrm{We}\mathrm{have}5-6x=0 \\ \Rightarrow -6x=-5 \\ \Rightarrow x=\frac{-5}{-6}=\frac{5}{6} \\ \therefore \frac{5}{6}\mathrm{is}\mathrm{the}\mathrm{zero}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{polynomial}. \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iv}\right)\mathrm{To}\mathrm{find}\mathrm{the}\mathrm{zero}\mathrm{of}p\left(y\right),\mathrm{we}\mathrm{will}\mathrm{solve}\mathrm{the}\mathrm{equation}p\left(y\right)=0. \\ \mathrm{We}\mathrm{have}y+1=0 \\ \Rightarrow y=-1 \\ \therefore -1\mathrm{is}\mathrm{the}\mathrm{zero}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{polynomial}. \end{gathered}$$

$$\begin{gathered} \left(\mathrm{v}\right)\mathrm{To}\mathrm{find}\mathrm{the}\mathrm{zero}\mathrm{of}p\left(m\right),\mathrm{we}\mathrm{will}\mathrm{solve}\mathrm{the}\mathrm{equation}p\left(m\right)=0. \\ \mathrm{We}\mathrm{have}m=0 \\ \therefore 0\mathrm{is}\mathrm{the}\mathrm{zero}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{polynomial}. \end{gathered}$$

$$\begin{gathered} \left(\mathrm{vi}\right)\mathrm{To}\mathrm{find}\mathrm{the}\mathrm{zero}\mathrm{of}q\left(y\right),\mathrm{we}\mathrm{will}\mathrm{solve}\mathrm{the}\mathrm{equation}q\left(y\right)=0. \\ \mathrm{We}\mathrm{have}4y=0 \\ \Rightarrow y=0 \\ \therefore 0\mathrm{is}\mathrm{the}\mathrm{zero}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{polynomial}. \end{gathered}$$