Question

26. 11 Uie Sun Olle ZCIUCU, puuuuu f(x)= ax2+bx+c are equal, and the sum of coefficients is 2, then find a. 27. Find the largest single-digit number by which the expression n - n is divisible for all possible integral values of 28. If f(x) = ax + bx + c is divided by x, X-2 and x + 3, the remainders comes out to be 7. 9 and 49 find 122 +59 + 2)2

JEE/Engineering Exams

Maths

Solution

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Method 1: Remember: The product of ( n ) number of consecutive positive integers is always divisible by ( n ! ) ( therefore n^{3}-n=nleft(n^{2}-1right)=n(n+1)(n-1) ) ( =(n-1) n(n+1) ) The above number: ( (n-1) n(n+1) ) is the product of three consecutive positive integers ( (n geq 2) ) which is divisible by ( 3 !=6 ) Hence, the number: ( n^{3}-n ) is divisible by 6 for all positive integers ( n )