Question

Total number of values of 'a' so that $x^2$ - x - a = 0 has integral roots, $aϵN$ & 5 < a < 99 is

• A. 2
• B. 4
• C. 5
• D. 8

Answer 1

The correct option is D

8

$x^2$ - x - a = 0
$\therefore \Delta =1-4(-a)\Rightarrow \Delta =1+4a$ = An odd number
$i.e\Delta =(1+2k{)}^2\text{(Because if root is an integer, Discriminant must be a perfect square)}i.e1+4a=1+4k^2+4k\Rightarrow a=k(k+1)$

$\therefore$ 8 cases only