How do you solve $7x ^ { 3} + 21x ^ { 4} = 0$ ?

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Answer 1 · 2018-03-09T03:25:51

See a solution process below:

First, factor out the common term $(7x^3)$ from each term on the left side of the equation:

$(7x^3 xx 1) + (7x^3 xx 3x) = 0$

$7x^3(1 + 3x) = 0$

Now, solve each term on the left for $0$ :

Solution 1:

$7x^3 = 0$

$(7x^3)/color(red)(7) = 0/color(red)(7)$

$x^3 = 0$

$root(3)(x^3) = root(3)(0)$

$x = 0$

Solution 2:

$1 + 3x = 0$

$1 - color(red)(1) + 3x = 0 - color(red)(1)$

$0 + 3x = -1$

$3x = -1$

$(3x)/color(red)(3) = -1/color(red)(3)$

$x = -1/3$

The Solution Set Is:

$x = {-1/3, 0}$

How do you solve 7x ^ { 3} + 21x ^ { 4} = 07x ^ { 3} + 21x ^ { 4} = 0?