JEE Quadratic#2

Algebra Level 3

If the equation $x^{2} +kx +k=0$ with $k$ as a parameter has exactly two distinct real roots (of $x$ ), find the smallest integral value of $\mid k \mid$ .

0 1 3 2

1 solution

Prakhar Bindal
Mar 4, 2015

You can simply put discriminant of the quadratic greater than zero you will get k = (-infinite,0) and (4,infinite) smallest integral value of mod k will occur when k = -1

A mathematical way to put it is,

$k\in (-\infty,0) \cup (4,+\infty)\\ \implies |k|\in (0,+\infty) \cup (4,+\infty)$

$\because~(4,+\infty)\subset (0,+\infty)$ , their union is simply the bigger set, i.e., $(0,+\infty)$ . Thus, we have,

$|k|\in (0,+\infty)\implies |k|\in \mathbb{R^+}$

The required value is $\left\lceil 0^+\right\rceil=\boxed{1}$

Prasun Biswas - 6 years, 3 months ago

JEE Quadratic#2

1 solution

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