Question

the coefficient of x in the quadratic equation x^2+px+q=0 was taken as 17 in place of 13, its roots were found to be -2 and -15. find the original roots.

Answer 1

$q=(-2)(-15)=30$

therefore the actual quadratic equation is
$x^2+13x+30=0$

which can be factored easily

Answer 2

x² + p x + q  = 0
   originally p = 13
   if  p  =  17,  then roots are  -2  and -15.  In that case the product of the roots q = 30.  That was correct it means.  Only the sum was wrongly written.

  so  q = (-2) (-15) = 30

now  the quadratic equation :  x² + 13 x + 30 = 0
          factors of 30  are    10 and 3  summing to 13.
         (x + 10) (x + 3) = 0
         original roots are  -3  and -10