in copying a quadratic equation of the form x + px + q = 0, the coefficient of x was wrongly written as - 10 in place of - 11 and the roots were found to be 4 and 6. The roots of the correct equation are (1) 8,3 (2) 4, 3 (3) 6,3 (4) 5,6

$$\begin{gathered} \mathrm{Sum} \mathrm{of} \mathrm{roots} \mathrm{are} \mathrm{wrong} \mathrm{but} \mathrm{product} \mathrm{of} \mathrm{roots} \mathrm{is} \mathrm{corect} \\ \mathrm{because} \mathrm{only} \mathrm{coeff}. \mathrm{of} \mathrm{x} \mathrm{is} \mathrm{wrongly} \mathrm{written} \\ \therefore \mathrm{Let} \mathrm{uses} \mathrm{be} \mathrm{x}, \mathrm{B} \\ \mathrm{\alpha }+\mathrm{\beta } = 11 \\ \mathrm{\alpha \beta }= 6\mathrm{x}4 =24 \\ \Rightarrow \mathrm{\alpha }+\mathrm{\beta }=11 \\ \mathrm{\alpha \beta }=24 \\ \mathrm{from} \mathrm{Observation}, \mathrm{we} \mathrm{can} \mathrm{say} \\ \mathbf{roots}\mathbf{ }\mathbf{are}\mathbf{ }\mathbf{,}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{\alpha }\mathbf{=}\mathbf{8}\mathbf{,}\mathbf{ }\mathbf{\beta }\mathbf{=}\mathbf{3}\mathbf{ }\mathbf{Ans} \end{gathered}$$