rahul and sachin made a mistake

Algebra Level 3

Sachin and Rahul attempted to solve a quadratic equation . Sachin made a mistake in writing down the constant term and ended up in roots (4,3) Rahul made a mistake in writing down coefficient of x to get roots (3,2). The correct roots of the equation are (p,q). What is p!+q!

NOTE : take the largest root as p


The answer is 721.

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1 solution

Aniket Kamble
Aug 1, 2015

Sachin got roots as (4,3) = (x-4)(x-3) = x^2 - 7x +12 ; here his constant term is wrong ; hence -7 is correct... and in rahul's case ; roots were (3,2) =(x-3)(x-2) =x^2 - 5x +6 ; here his constant term is right and -5 is wrong..... thus overall correct equation would be X^2 - 7x + 6 , roots for this equation are :- (x-6)(x-1) , x-6 =0 , x= 6 , x-1=0, x= 1 hence P = 6, Q= 1 now, P! + Q! = 6! + 1! =720 +1=721

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