Q2 FACTORS - MULTIPLES

m is the smallest positive integer such that for any integer n > m, the quantity n³-7n^2+11n-5 is positive. What is the value of m?

(a). 4

(b). 5

(c), 8

Option (d)

n=1 is a root of the equation

(n−1)(n^2−6n+5)=(n−1)(n-1)(n−5)

Now, n−12 is always positive.

Now, for n < 5, the expression gives a negative quantity.

Therefore, the least value of n will be 6. Hence m = 7 .

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