How do you solve $9 x^{4} + 18 x^{3} + 9 x^{2} = 0$ $9x ^ { 4} + 18x ^ { 3} + 9x ^ { 2} = 0$ ?

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How do you solve $9 x^{4} + 18 x^{3} + 9 x^{2} = 0$ $9x ^ { 4} + 18x ^ { 3} + 9x ^ { 2} = 0$ ?

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Answer 1 · 2017-10-25T02:43:28

$x = - 1, - 1, 0, 0$ $x = -1, -1, 0, 0$

Explanation:

First, begin by factoring as much as possible from each term of the equation on the left hand side:

$9 x^{4} + 18 x^{3} + 9 x^{2} = 0$ $9x^4 + 18x^3 + 9x^2 = 0$

$(9 x^{2}) (x^{2} + 2 x + 1) = 0$ $(9x^2)(x^2 + 2x + 1) = 0$

Now factor the quadratic:

$(9 x^{2}) (x + 1) (x + 1) = 0$ $(9x^2)(x+1)(x+1) = 0$

Since we know the product of the three terms on the left comes out to 0, we know that any one of those terms evaluating to 0 will be a solution of the equation. Thus, we solve each factor separately to determine all possible solutions for $x$ $x$ :

$9 x^{2} = 0$ $9x^2 = 0$

$x^{2} = 0$ $x^2 = 0$

$x = \pm 0 \Rightarrow x = 0 (Multiplicity 2)$ $x = +- 0 => x = 0 " (Multiplicity 2)"$

$x + 1 = 0 \Rightarrow x = - 1$ $x+1 = 0 => x = -1$

$x + 1 = 0 \Rightarrow x = - 1$ $x + 1 = 0 => x = -1$

We get four roots: $x = - 1, - 1, 0, 0$ $x = -1, -1, 0, 0$ .

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How do you solve $9 x^{4} + 18 x^{3} + 9 x^{2} = 0$ $9x ^ { 4} + 18x ^ { 3} + 9x ^ { 2} = 0$ ?

1 Answer

Explanation:

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How do you solve 9x4+18x3+9x2=09x ^ { 4} + 18x ^ { 3} + 9x ^ { 2} = 0?

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How do you solve $9 x^{4} + 18 x^{3} + 9 x^{2} = 0$ $9x ^ { 4} + 18x ^ { 3} + 9x ^ { 2} = 0$ ?