Advertisement Remove all ads

Find the value of: 2x3 – 11x2 + 44x + 27, if x = 253-4i - Mathematics

Advertisement Remove all ads
Advertisement Remove all ads
Sum

Find the value of: 2x3 – 11x2 + 44x + 27, if x = `25/(3 - 4"i")`

Advertisement Remove all ads

Solution

x = `25/(3 - 4"i")`

∴ x = `(25(3 + 4"i"))/((3 - 4"i")(3 + 4"i")`

= `(25(3 + 4"i"))/(9 - 16"i"^2)`

= `(25(3 + 4"i"))/(9 - 16(-1))`                 ...[∵ i2 = – 1]

= `(25(3 + 4"i"))/25`

∴ x = 3 + 4
∴ x – 3 = 4i
∴ (x –  3)2 = 16i2
∴ x2 –  6x + 9 = 16(–  1)      ...[∵ i2 = – 1]
∴ x2 – 6x + 25 = 0

                      2x + 1
`x^2 – 6x + 25")"overline(2x^3 - 11x^2 + 44x + 27)"`
                      2x3 – 12x2 + 50x
                    –      +         –                      
                                   x2 – 6x + 27
                                  x2 – 6x + 25
                              –      +      –                
                                                  2

∴ 2x3 – 11x2 + 44x + 27
= (x2 – 6x + 25) (2x + 1) + 2
= 0.(2x + 1) + 2            ...[From (i)]
= 0 + 2
= 2

Concept: Algebra of Complex Numbers
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 3 Complex Numbers
Exercise 3.1 | Q 9. (ii) | Page 38

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×