Solve for the roots of x in each of the equations below. a. x4 - 81 = 0 b. x4 + 10x2 + 25 = 0 c. x4 - x2 - 6 = 0

a) 0 = x⁴ - 81

   0 = (x² - 9)(x² + 9)

   0 = (x - 3)(x + 3)(x² + 9)  

0 = x - 3  ,  0 = x + 3  ,  0 = x² + 9

  x = 3    ,       x = -3   ,      x² = -9 →  x = √-9  →  x = +/- 3i

real roots 3, 3  ; complex roots 3i, -3i

b) 0 = x⁴ + 10x² + 25

   0 = (x² + 5)²

0 = x² + 5

x² = -5  →  x = +/-√-5  →  x = +/- i√5

no real roots  ; complex roots i√5, -i√5

c) 0 = x⁴ - x² - 6

  0 = (x² - 3)(x² + 2)

0 = x² - 3                       0 = x² + 2

x² = 3  → x = +/-√3        x² = -2  →  x = +/-√-2  →  x = +/-i√2

real roots √3, -√3; complex roots i√2, -i√2

what graph

step-by-step explanation:

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: