qanda-logo
apple logogoogle play logo

Calculator search results

Formula
Solve a quadratic inequality
Answer
circle-check-icon
expand-arrow-icon
Graph
$- 3 x ^ { 2 } + x - 3 < 0$
$- 3 x ^ { 2 } + x - 3 < 0$
Solution of inequality
$x \in \mathbb{R} \left ( \text{It holds for all real numbers} \right )$
$-3x ^{ 2 } +x-3 < 0$
$x \in \mathbb{R} \left ( \text{It holds for all real numbers} \right )$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } < \color{#FF6800}{ 0 }$
$ $ Change the symbol of the inequality of both sides, and reverse the symbol of the inequality to the opposite direction $ $
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } > \color{#FF6800}{ 0 }$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } > \color{#FF6800}{ 0 }$
$ $ Convert the inequality to a quadratic equation to find $ x_{1}, x_{2}$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } = \color{#FF6800}{ 0 }$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } = \color{#FF6800}{ 0 }$
$ $ Calculate using the quadratic formula $ $
$x \in \emptyset \left ( \text{Do not have the solution} \right )$
$\color{#FF6800}{ x } \in \emptyset \left ( \text{Do not have the solution} \right )$
$ $ If there is no real root, the left side of the inequality has always a positive value or a negative value depending on coefficient of the leading highest term a(= $ 3 $ ) of $ ax^{2}+bx+c=0$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } > \color{#FF6800}{ 0 }$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } > \color{#FF6800}{ 0 }$
$ $ Since the coefficient of the leading highest term (= $ 3 $ ) is $ $ (+) $ $ , the left side of the inequality is always $ $ (+) $ $ So this inequality is $ $ TRUE $ $ regardless of the value of $ x$
$\color{#FF6800}{ x } \in \mathbb{R} \left ( \text{It holds for all real numbers} \right )$
$ $ 그래프 보기 $ $
Inequality
Have you found the solution you wanted?
Try again
Try more features at Qanda!
Search by problem image
Ask 1:1 question to TOP class teachers
AI recommend problems and video lecture
apple logogoogle play logo