Answer:
sum of the roots: [tex]x_1+x_2=4\frac12[/tex]
product of the roots: [tex]x_1x_2=-5[/tex]
Step-by-step explanation:
[tex]2x^2-9x-10=0\quad\implies\quad a=2\,,\ b=-9\,,\ c=-10[/tex]
[tex]b^2-4ac=(-9)^2-4(2)(-10)=81+80=161>0[/tex]
From Vieta's formulas applied to quadratic polynomial we have:
if [tex]b^2-4ac\geqslant0[/tex] then
sum of roots: [tex]x_1+x_2=-\dfrac ba=-\dfrac{-9}2=4\frac12[/tex]
product of the roots: [tex]x_1x_2=\dfrac ca=\dfrac{-10}2=-5[/tex]
