Question

Assertion ($A$): lf $x^2-7x+10<0$, then $x\in (2,5)$ .
Reason ($R$): lf $a$ and $a{x}^2+bx+c$ have opposite signs and $b^2-4ac>0$ then $x$ lies between the roots of $a{x}^2+bx+c=0$ for $a{x}^2+bx+c<0$

• A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A$ .
• B. Both $A$ and $R$ are true, but $R$ is not the correct explanation of $A$ .
• C. $A$ is true but $R$ is false .
• D. $A$ is false but $R$ is true .

Answer 1

The correct option is A Both $A$ and $R$ are true and $R$ is the correct explanation of $A$ .

$(x-2)(x-5)<0$
$\forall x\in (2,5)$
$\therefore$ The region lies between the curve and is below x-axis for $x\in (2,5)$ .