Question

Solve the polynomial inequality. Express the solution set in interval notation.

$13x^2-5x\le 0$

• A. $(-\infty ,0)\cup (\frac{5}{13},\infty )$
• B. $(0,-\frac{5}{13})$
• C. $(-\infty ,0)\cup [-\frac{5}{13},\infty ]$
• D. $[0,\frac{5}{13}]$
  

Answer 1

The correct option is D $[0,\frac{5}{13}]$

Given,
$13x^2-5x\le 0$

$\Rightarrow x(13x-5)\le 0$ ...(i)

Two cases arises:
Case I:
(i) holds,
if $x\ge 0$ and $(13x-5)\le 0$

if $x\ge 0$ and $x\le \frac{5}{13}$

if $0\le x\le \frac{5}{13}$

if$x\in [0,\frac{5}{13}]$

Case II:
(i) holds,
if $x\le 0$ and $(13x-5)\ge 0$

if $x\le 0$ and $x\ge \frac{5}{13}$

no such x exist.
On combining case I and II, we get

$x\in [0,\frac{5}{13}]$