# 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

$\mathrm{Sum}\mathrm{of}\mathrm{roots}\mathrm{are}\mathrm{wrong}\mathrm{but}\mathrm{product}\mathrm{of}\mathrm{roots}\mathrm{is}\mathrm{corect}\phantom{\rule{0ex}{0ex}}\mathrm{because}\mathrm{only}\mathrm{coeff}.\mathrm{of}\mathrm{x}\mathrm{is}\mathrm{wrongly}\mathrm{written}\phantom{\rule{0ex}{0ex}}\therefore \mathrm{Let}\mathrm{uses}\mathrm{be}\mathrm{x},\mathrm{B}\phantom{\rule{0ex}{0ex}}\mathrm{\alpha}+\mathrm{\beta}=11\phantom{\rule{0ex}{0ex}}\mathrm{\alpha \beta}=6\mathrm{x}4=24\phantom{\rule{0ex}{0ex}}\Rightarrow \mathrm{\alpha}+\mathrm{\beta}=11\phantom{\rule{0ex}{0ex}}\mathrm{\alpha \beta}=24\phantom{\rule{0ex}{0ex}}\mathrm{from}\mathrm{Observation},\mathrm{we}\mathrm{can}\mathrm{say}\phantom{\rule{0ex}{0ex}}\mathbf{roots}\mathbf{}\mathbf{are}\mathbf{}\mathbf{,}\mathbf{}\mathbf{}\mathbf{}\mathbf{\alpha}\mathbf{=}\mathbf{8}\mathbf{,}\mathbf{}\mathbf{\beta}\mathbf{=}\mathbf{3}\mathbf{}\mathbf{Ans}$