Question

The roots of the equation $x^2+2(a-3)x+9=0$ lies between $-6$ and $1$ then $\left[a\right]=$________ , where $[.]$ denotes greatest integer function $x$.

• A. $6$
• B. $12$
• C. $19$
• D. $3$

Answer 1

The correct option is A

$6$

$△\ge 0,f(-6)>0,f\left(1\right)>0$ ,

$\Rightarrow -6<\frac{\alpha +\beta }{2}<1$

$\Rightarrow \left[a\right]=6$