# Rohans mother is 26 years older than him. The product of their ages 3 years from now will be 360. Formulate the quadratic equation to find their ages and find the present age of mother.

$Let\;Rohan\;present\;age\;be\;x\;years.\;Then,\;age\;of\;his\;mother\;is\;(x+26)\;years\\*Age\;of\;Rohan\;after\;3\;years=(x+3)\;years\\* After\;3\;years\;the\;age\;of\;mother=(x+26+3)\;years=(x+29)\;years\\* It\;is\;given\;that\;after\;3\;years\;from\;now,\;the\;product\;of\;ages\;of\;both\;will\;be\;360\;years\\*\therefore (x+3)(x+29)=360\\* The\;required\;equation\;is\Rightarrow x^2+32x-273=0\\*\Rightarrow (x+39)(x-7)=0\\*\therefore x=-39\;and\;x=7\\*\because x\;can\;not\;be\; negative,\therefore x=7\\*\therefore\;present\;age\;of\;mother=7+26=33\;years$

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