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Find the roots of the function f(x) = 3x4 - 48.

Sagot :

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Answer:

[tex]x=\pm 2\text{ or } x = \pm 2i[/tex]

Step-by-step explanation:

We are given:

[tex]0=3x^4-48[/tex]

Factor:

[tex]0=3(x^4-16)[/tex]

Difference of Two Squares:

[tex]0=3(x^2-4)(x^2+4)[/tex]

Zero Product Property:

[tex](x^2-4)=0\text{ or } x^2+4=0[/tex]

Solve:

[tex]x^2=4\text{ or } x^2=-4[/tex]

Take the square root. Since we are taking an even-root, it requires plus/minus:

[tex]x=\pm 2\text{ or } x = \pm 2i[/tex]

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