Question

if a b are zeros of polynomial p(x) = 5 x square + 5 x + 1 then find the value of (1) a square + b square (2) a square^-1 + b square ^-1

Answer 1

$p(x)=5x^2+5x+1\\ a+b=-\frac{5}{5}=-1\\ ab=\frac{1}{5}\\ a^2+b^2\\ =(a+b)^2-2ab\\ =1-\frac{2}{5}\\ =\frac{3}{5}\\ \frac{1}{a}+\frac{1}{b}\\ =\frac{a+b}{ab}\\ =\frac{-1}{\frac{1}{5}}\\ =-5$