Question

If $p(p+q+r)<0<(p+q+r)r$, then

• A. At least one of the roots lies in $(0,1)$
• B. One root is less than $0$, the other is greater than $1$
• C. Exactly one of the roots lies in $(0,1)$
• D. Both the roots lie in $(0,1)$

Answer 1

The correct option is B One root is less than $0$, the other is greater than $1$

$pf\left(1\right)<0\&f\left(0\right).f\left(1\right)>0$
$\Rightarrow pf\left(1\right)<0$ and $pf\left(0\right)<0$
Hence, both the numbers $0$ and $1$ lie between the roots.