Question

(i) If $p\left(x\right)=2+5x$ then $p\left(2\right)+p\left(-2\right)$ $-p\left(1\right)$.

(ii) $p\left(x\right)=2x^2-5\sqrt{3}x+5$ then $p\left(5\sqrt{3}\right)$.

Answer 1

(i)
$$\begin{gathered} p\left(x\right)=2+5x \\ \therefore p\left(2\right)=2+5\times 2=2+10=12 \\ p\left(-2\right)=2+5\times \left(-2\right)=2-10=-8 \\ p\left(1\right)=2+5\times 1=2+5=7 \end{gathered}$$
$\therefore p\left(2\right)+p\left(-2\right)-p\left(1\right)=12+\left(-8\right)-7=12-8-7=12-15=-3$

(ii)
$p\left(x\right)=2x^2-5\sqrt{3}x+5$
$$\begin{gathered} \therefore p\left(5\sqrt{3}\right)=2\times {\left(5\sqrt{3}\right)}^2-5\sqrt{3}\times 5\sqrt{3}+5 \\ =2\times 75-25\times 3+5 \\ =150-75+5 \\ =80 \end{gathered}$$