Question

If the smaller root of the equation $x^2-ax+4=0$ lies between $-1$ and $-2$, then belongs to

• A. $(0,-5)$
• B. $(0,3)$
• C. $(-\infty ,-3)$
• D. $(-\infty ,-3)\cup (0,\infty )$

Answer 1

The correct option is A $(0,-5)$

Since smaller root of equation

$x^2-ax+4=0$ lies between $(-1,-2)$

$\therefore f(-2)>0$

$\therefore f(-1)>0$

$\therefore f(-2)=(-2{)}^2+a(-2)-4$

$\therefore f(-2)=4-4-2a$

$\therefore f(-2)=-2a$

$\therefore -2a>0$

$\therefore (a<0)----\left(1\right)$

$\therefore f(-1)=1+a+4$

$\therefore f(-1)=5+a$

$\therefore 5+a<0$

$\therefore a<-5----\left(2\right)$

$\therefore$ from $\left(1\right)$ & $\left(2\right)$

$a<-5$