ANSWER:
A)
The sum of roots: 2.5
The product of the root: 0.5
B)
The sum of roots: -8
The product of the root: -3
STEP-BY-STEP EXPLANATION:
The sum of the roots can be obtained using the following expression:
[tex]x_1+x_2=-\frac{b}{a}[/tex]We calculate in each case:
[tex]\begin{gathered} 2x^2-5x+1=0\rightarrow a=2,b=-5 \\ \\ x_1+x_2=-\frac{-5}{2}=2.5 \\ \\ x^2+8x-3=0\rightarrow a=1,b=8 \\ \\ x_1+x_2=-\frac{8}{1}=-8 \end{gathered}[/tex]Now, in the case of the product of roots, we calculate it by means of the following expression:
[tex]x_1\cdot x_2=\frac{c}{a}[/tex]We calculate in each case:
[tex]\begin{gathered} 2x^2-5x+1=0\rightarrow a=2,c=1 \\ \\ x_1\cdot x_2=\frac{1}{2}=0.5 \\ \\ x^2+8x-3=0\rightarrow a=1,c=-3 \\ \\ x_1\cdot x_2=\frac{-3}{1}=-3 \end{gathered}[/tex]