The coefficient of x in the equation ${\mathrm{x}}^2+\mathrm{px}+\mathrm{q}=0$ was taken as 17 in place of 13 its roots were found to be - 2 and -15. The roots of the original equation are

 Let the equation (incorrectly written form) be ${\mathrm{x}}^2+17\mathrm{x}+\mathrm{q}=0$
Since, roots are -2 ,-15 .
$\therefore \mathrm{q}=30$
So, correct equation is ${\mathrm{x}}^2+13\mathrm{x}+30=0$
$\begin{array}{ccc}\Rightarrow & {\mathrm{x}}^2+10\mathrm{x}+3\mathrm{x}+30& =0\\ \Rightarrow & (\mathrm{x}+3)(\mathrm{x}+10)=0& \\ \Rightarrow & \mathrm{x}=-3,-10& \end{array}$