Question

Assertion($A$) : $x^2+x+1$ is greater than zero for all real $x$ .
Reason ($R$) : When $b^2-4ac<0$. Then $a{x}^2+bx+c$ have the same sign for all real values of $x$ .

• A. Both $A$ and $R$ are true and $R$ is the correct explanation of A .
• B. Both $A$ and $R$ are true and $R$ 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 .

$x^2+x+1=0$

$b^2-4ac=1-\mathrm{4.1.1}=-3<0$

and $a>0$

so $x^2+x+1>0$