Question

Total number of integral values of $a$ so that $x^2-(a+1)x+a-1=0$ has integral roots is equal to

• A. $1$
• B. $2$
• C. $4$
• D. None of the above.

Answer 1

The correct option is A $1$

For integer roots $b^2-4ac$ should be a perfect square.

$x^2-(a+1)x+(a-1)=0⟹b^2-4ac={(a+1)}^2-4(a-1)=a^2-2a+5or{p}^2=a^2-2a+5\therefore fora=1,a^2-2a+5$

is a perfect square.

$\therefore$ for $a=1,a^2-2a+5=4$,

Only one integral value of $a$.