cat 2022 Question 5

Question

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

Accepted Answer

$b^2$ < $4ac$ means that the discriminant is less than 0. Therefore, f(x)>0 for all x if the coefficient of $x^2$ is positive, and f(x)<0 for all x if the coefficient of $x^2$ is negative.

We are given that f(m)<0 and m is an integer.

So the set containing values of m will either be empty if the coefficient of $x^2$ is positive, or it will be a set of all

Question 5.

Question Explanation