Wraith Wraith
  • 09-11-2023
  • Mathematics
High School

What are the roots of [tex]3x^4 - 21x^2 + 18 = 0[/tex]?

Answer :

sqdancefan sqdancefan
  • 30-07-2023

Answer:

{-√6, -1, 1, √6}

Step-by-step explanation:

You want the roots of the quartic 3x^4-21x^2+18.

Factors

We can find the roots by factoring to linear factors:

= 3(x^4 -7x^2 +6)

= 3(x^2 -6)(x^2 -1) . . . . . . . 6 = (-1)(-6) are factors with a sum of -7

= 3(x -√6)(x +√6)(x -1)(x +1) . . . . . a^2 -b^2 = (a -b)(a +b)

The roots of the quartic are ±√6 and ±1.

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