Algebra

Polynomials

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

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

In $f(x)$ , we know that $a^2$ will always be positive, ergo, it'll be greater than 0.

Solution figure for IPMAT Indore 2025 MCQ question 14 (Algebra)

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).

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Let f(x)=a2x2+2bx+cf(x) = a^2x^2 + 2bx + cf(x)=a2x2+2bx+c where, a≠0a \neq 0a=0, b,cb, cb,c are real numbers and xxx is a real variable then

Solution

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IPMAT Indore Past Year Questions (Topic-Wise)

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