we should find the roots of \( p(x) \).
we have:
\( A=3 , B=-4 , C=1 \)
\( \Delta=B^2-4AC=(-4)^2-4(3)(1)=16-12=4 \)
\( a , b=\frac{-b \pm \sqrt{\Delta}}{2a} \)
\( a , b=\frac{4 \pm \sqrt{4}}{2(3)} \)
\( a=\frac{4+2}{6}=1 \)
\( b=\frac{4-2}{6}=\frac{1}{3} \)
we should placement \( a \) and \( b \) in the part (i) and (ii). we have:
(i)
\( a^2 \times b^2=1^2 \times {\frac{1}{3}}^2=1 \times \frac{1}{9}=\frac{1}{9} \)
(ii)
\( a^2 \times (b+a) \times b^2=1^2 \times (\frac{1}{3}+1) \times {\frac{1}{3}}^2=1 \times \frac{4}{3} \times \frac{1}{9}=\frac{4}{27} \)
