How do you find all zeros with multiplicities of $f (x) = 3 x^{4} - 14 x^{2} - 5$ $f(x)=3x^4-14x^2-5$ ?

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How do you find all zeros with multiplicities of $f (x) = 3 x^{4} - 14 x^{2} - 5$ $f(x)=3x^4-14x^2-5$ ?

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Answer 1 · 2017-02-13T23:54:00

$x = \pm \frac{\sqrt{3}}{3} i$ $x = +-sqrt(3)/3i$

$x = \pm \sqrt{5}$ $x = +-sqrt(5)$

Explanation:

$f (x) = 3 x^{4} - 14 x^{2} - 5$ $f(x) = 3x^4-14x^2-5$

$f (x) = (3 x^{4} - 15 x^{2}) + (x^{2} - 5)$ $color(white)(f(x)) = (3x^4-15x^2)+(x^2-5)$

$f (x) = 3 x^{2} (x^{2} - 5) + 1 (x^{2} - 5)$ $color(white)(f(x)) = 3x^2(x^2-5)+1(x^2-5)$

$f (x) = (3 x^{2} + 1) (x^{2} - 5)$ $color(white)(f(x)) = (3x^2+1)(x^2-5)$

$f (x) = ({(\sqrt{3} x)}^{2} - i^{2}) (x^{2} - {(\sqrt{5})}^{2})$ $color(white)(f(x)) = ((sqrt(3)x)^2-i^2)(x^2-(sqrt(5))^2)$

$f (x) = (\sqrt{3} x - i) (\sqrt{3} x + i) (x - \sqrt{5}) (x + \sqrt{5})$ $color(white)(f(x)) = (sqrt(3)x-i)(sqrt(3)x+i)(x-sqrt(5))(x+sqrt(5))$

Hence zeros:

$x = \pm \frac{i}{\sqrt{3}} = \pm \frac{\sqrt{3}}{3} i$ $x = +-i/sqrt(3) = +-sqrt(3)/3i$

$x = \pm \sqrt{5}$ $x = +-sqrt(5)$

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How do you find all zeros with multiplicities of $f (x) = 3 x^{4} - 14 x^{2} - 5$ $f(x)=3x^4-14x^2-5$ ?

1 Answer

Explanation:

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Humanities

... and beyond

How do you find all zeros with multiplicities of f(x)=3x4−14x2−5f(x)=3x^4-14x^2-5?

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Explanation:

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How do you find all zeros with multiplicities of $f (x) = 3 x^{4} - 14 x^{2} - 5$ $f(x)=3x^4-14x^2-5$ ?