Question

2) A equação x² - 6x - 16 = 0 tem duas raizes diferentes, expressas por x'e x". Sem resolver a equação,determine o valor de:

a) x´ + x´´
b) x´ . x´´
c) ⅟x´ + ⅟x´´

Answer 1

$\large\boxed{\begin{array}{l}\rm x^2-6x-16\\\sf a)~\rm x'+x''=-\dfrac{b}{a}\\\\\rm x'+x''=-\dfrac{-6}{1}=6\\\\\sf b)~\rm x'\cdot x''=\dfrac{c}{a}\\\\\rm x'\cdot x''=\dfrac{-16}{1}=-16\\\\\sf c)~\rm\dfrac{1}{x'}+\dfrac{1}{x''}=\dfrac{x'+x''}{x'\cdot x''}\\\\\rm \dfrac{1}{x'}+\dfrac{1}{x''}=\dfrac{6\div2}{-16\div2}\\\\\rm\dfrac{1}{x'}+\dfrac{1}{x''}=-\dfrac{3}{8}\end{array}}$