Question

4) x = -2 and x = R are the solutions of Ax^2+9x-2=0, what are the values of R and A?5) Find all complex pairs (x,y) such that x + y = -6 and Xy=10

Answer 1

$\begin{gathered} \text{Equation is Ax}^2+9x-2=0 \\ \text{put x=-2 in above equation} \\ A(-2)^2+9(-2)-2=0 \\ 4A-18-2=0 \\ 4A-20=0 \\ 4A=20 \\ A=\frac{20}{4} \\ A=5 \\ \text{Put x= R in above eqution } \\ A(R)^2+9R-2=0 \\ \text{Put the value of A also} \\ 5R^2+9R-2=0 \\ 5R^2+10R-R-2=0 \\ 5R(R+2)-1(R+2)=0 \\ (5R-1)(R+2)=0 \\ R=-2\text{ and R=}\frac{\text{1}}{5} \end{gathered}$