Question

For how many values of the coefficient $a$ do the equation $x^2+ax+1=0,x^2-x-a=0$ have a common real solution?

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is B $1$

$x^2+ax+1=0$___(1)

$x^2-x-a=0$____(2)

They have one conman solution

$x^2+ax+1=0$

$x^2-(x-a)=0$

_______________

$0+(a+1)x+(1+x)=0$

$x=-1$

$x^2+ax+1=0$

$(-1{)}^2-1(a)+1=0$

$2-a=0$ $\Rightarrow a=2$