IPMAT Indore 2025 (MCQ) - Let f(x) = a^2x^2 + 2bx + c where, a ≠ 0, b, c are real numbers and x is a real variable then | PYQs + Solutions

IPMAT Indore 2025

Algebra

Quadratic Equations

Easy

Let $f(x) = a^2x^2 + 2bx + c$ where, $a \neq 0$ , $b, c$ are real numbers and $x$ is a real variable then

f(x)

has a maximum and a minimum

f(x)

has a minimum and no maximum

f(x)

has a maximum and no minimum

f(x)

has no minimum and no maximum

✅ Correct Option: 2

f(x) = a^2x^2 + 2bx + c

f(x)

, we know that

a^2

will always be positive, ergo, it'll be greater than 0.

Hence, the quadratic function will be U-shaped (opening upward).

Thus, it has a minimum point but no maximum point (goes all the way till infinity).