Wraith Wraith
  • 24-08-2023
  • 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.

Answer Link

Other Questions

Divide: [tex]\[ 913 \div 280, 291 \][/tex] Submit your answer.
A drill rod is used with an air hammer for making holes
Multiply the polynomials: [tex]\left(5x^2 + 2x + 8\right)(7x - 6)[/tex] A. [tex]35x^3
Convert 1500 micrometers to meters.
Select the correct answer. The average summer temperature in Anchorage is [tex]69^{\circ}
2.00 liters of nitrogen at 215.91 torr is mixed with 2.00 liters
You use 24 tokens to play arcade games that each cost 4
Calculate the height of the demonstration. A) 17.136 meters B) 1.008 meters
Discuss the loyalty of customers to Red Bull products: 1. **High Loyalty**:
What is the average IQ for a 12-year-old boy?
What is the rule? Convert the following measurements: - 100 cm to
Subtract and simplify the expression: [tex] \[ \left(3x^4 + 9x^3 - 5\right)
What class of fire extinguisher is used for cooking fires involving combustible
What equation represents the statement "the sum of two consecutive integers is
Which expression does the graphic represent? - 8 positive tiles with 1