Question

If the range of $k$ for which the quadratic equation polynomial $f(x)=k x^2-(2 k+3) x+6$ is positive for exactly three negative integral values of $x$ is $(a, b]$, then $a-4 b$ equals

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (B)

Clearly, $k <0$
$kx ^2-2 kx -3 x +6=0$
$( kx -3)( x -2)=0 \Rightarrow$ roots are $\frac{3}{ k }, 2$
$\frac{3}{ k } \in[-4,-3) \Rightarrow k \in\left(-1, \frac{-3}{4}\right] $
$\therefore a -4 b =2$