Quadratic Functions

Question

7

Use the quadratic formula to solve the equation .

Enter multiple answers as a list separated by commas. Example: 

Answer 1

Quadratic Formula : (-b ± √b² - 4ac) / 2a

9x² - 24x + 41 = 0

a = 9

b = -24

c = 41

x = (-(-24) ± √(-24)² - 4(9)(41)) / 2(9)

Split into two equations:

x₁ = (-(-24) + √(-24)² - 4(9)(41)) / 2(9)

= (24 + √(-24)² - 4(9)(41)) / 2(9)

= (24 + √576 - 1476) / 18

= (24 + √-900) / 18

= (24 + i√900) / 18

= (24 + 30i) / 18

= (6(4 + 5i)) / 18

= (4 + 5i) / 3

= 4/3 + 5i/3

x₂ = (-(-24) - √(-24)² - 4(9)(41)) / 2(9)

= (24 - √(-24)² - 4(9)(41)) / 2(9)

= (24 - √576 - 1476) / 18

= (24 - √-900) / 18

= (24 - i√900) / 18

= (24 - 30i) / 18

= (6(4 - 5i)) / 18

= (4 - 5i) / 3

= 4/3 - 5i/3