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Formula
Solve the cubic equation
Answer
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Graph
$y = x ^ { 3 }$
$y = - 27$
$x$Intercept
$\left ( 0 , 0 \right )$
$y$Intercept
$\left ( 0 , 0 \right )$
Derivative
$3 x ^ { 2 }$
Seconde derivative
$6 x$
Local Maximum
$\left ( 0 , 0 \right )$
Point of inflection
$\left ( 0 , 0 \right )$
$x ^{ 3 } = -27$
$x = - 3$
Solve the cubic equation
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } = \color{#FF6800}{ - } \color{#FF6800}{ 27 }$
$ $ Do the cube root on both sides of the equation $ $
$\color{#FF6800}{ x } = \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ - } \color{#FF6800}{ 27 } }$
$x = \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ - } \color{#FF6800}{ 27 } }$
$ $ The square root of a negative and odd root is always negative $ $
$x = \color{#FF6800}{ - } \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ 27 } }$
$x = - \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ 27 } }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$x = - \color{#FF6800}{ 3 }$
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