Maharashtra State BoardHSC Commerce 11th
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Find the value of : x3 – 5x2 + 4x + 8, if x = 103-i - Mathematics and Statistics

Sum

Find the value of :  x3 – 5x2 + 4x + 8, if x = `10/(3 - "i")`

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Solution

x = `10/(3 - "i")`

∴ x = `(10(3 + "i"))/((3 - "i")(3 + "i")`

= `(10(3 + "i"))/(9 - "i"^2)`

= `(10(3 + "i"))/(9 - (- 1)`          ...[∵ i2 = – 1]

= `(10(3 + "i"))/10`

∴ x = 3 + i
∴  x –  3 = i
∴ (x –  3)2 = i2
∴ x2 –  6x + 9 = –  1            ...[∵ i2 = – 1]
∴ x2 –  6x + 10 = 0            ...(i)

                       x + 1
`x^2 – 6x + 10")"overline(x^3 + 5x^2 + 4x + 8)"`
                        x3 – 6x2 + 10x
                        –      +       –              
                                x2 – 6x + 8
                                x2 – 6x + 10
                              –      +       –         
                                               –  2

∴ x3 – 5x2 + 4x + 8
= (x2 – 6x + 10)(x + 1) – 2
= 0. (x + 1) – 2                        ...[From (i)]
= 0 – 2
∴ x3 – 5x2 + 4x + 8 = – 2.

  Is there an error in this question or solution?
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 3 Complex Numbers
Miscellaneous Exercise 3 | Q 5. (ii) | Page 43
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