JEE Main 2026 Apr 2 Shift 1, Mathematics Q23: Quadratic Expressions

JEE Main2026Apr 2, Shift 1Mathematics

Let $a, b, c \in {1, 2, 3, 4}$ . If the probability that $a x^{2} + 22 b x + c > 0$ for all $x \in R$ , is $\frac{m}{n}$ , $g cd (m, n) = 1$ , then $m + n$ is equal to _______.

Your answer

Solution

$8b^2-4ac<0$

$\Rightarrow$ $ 2b^2< ac$

$b$	$a$	Possible values of $c$	Count
$1$	$1$	$3, 4$	$2$
$1$	$2$	$2, 3, 4$	$3$
$1$	$3$	$1, 2, 3, 4$	$4$
$1$	$4$	$1, 2, 3, 4$	$4$
$2$	$3$	$3, 4$	$2$
$2$	$4$	$3, 4$	$2$
Total			$17$

Required probability $= \dfrac{17}{64} = \dfrac{m}{n}$

$∴ m + n = 17 + 64 = 81$

$81$

Concept behind this question

Quadratic ExpressionsNotes, formulas and examples →

Practice more Mathematics

Concept-wise practice with instant solutions on Fundamenthol.

Start practicing →