Question

If the equation $x^2+2x-n=0$ has integral roots, then number of values of $n$ between $1$ & $125$ are

• A. $10$
• B. $8$
• C. $7$
• D. $6$

Answer 1

Answer: (A)

The equation $x^2+2x-n=0$ has integral roots , we need all values of $n(1<n<125)$ for which roots of the equations are integers
Here n represents the product of roots, therefore we need those values of n for which product of roots cannot exceed $125$
Now, from given equation we have
$n=x^2+2x=x(x+2)$
$\therefore n=x(x+2)$
$=\{1\times 3,2\times 4,3\times 5,4\times 6,5\times 7,6\times 8,7\times 9,8\times 10,9\times 11,10\times 12$, and the product of next pair $11\times 13>125\}$
$\therefore$ Number of values of $n$ between $1$ & $125$ are $10$