CAT 2022 Slot 1 QA Question 19: Let $a, b, c$ be non-zero real numbers such that $b^2

Question

Let $a, b, c$ be non-zero real numbers such that $b^2 < 4ac$, and $f(x) = ax^2 + bx + c$. If the set $S$ consists of all integers $m$ such that $f(m) < 0$, then the set $S$ must necessarily be

Accepted Answer

$b^2 
$\Rightarrow b^2 - 4ac 
So the quadratic has negative discriminant and no real roots. Also, since $b^2$ is non-negative and $b^2  0$, so $a$ and $c$ have the same sign.
A quadratic with no real roots has the same sign for all real $x$. Its sign is the sign of $a$.
If $a > 0$, then $f(x) > 0$ f

Let a,b,ca, b, ca,b,c be non-zero real numbers such that b2<4acb^2 < 4acb2<4ac, and f(x)=ax2+bx+cf(x) = ax^2 + bx + cf(x)=ax2+bx+c. If the set SSS consists of all integers mmm such that f(m)<0f(m) < 0f(m)<0, then the set SSS must necessarily be

Let $a, b, c$ be non-zero real numbers such that $b^2 < 4ac$ , and $f(x) = ax^2 + bx + c$ . If the set $S$ consists of all integers $m$ such that $f(m) < 0$ , then the set $S$ must necessarily be