Find the value of: x3 – 3x2 + 19x – 20, if x = 1 – 4i - Mathematics and Statistics

प्रश्न

Find the value of: x³ – 3x² + 19x – 20, if x = 1 – 4i

बेरीज

उत्तर

x = 1 – 4i

∴ x – 1 = – 4i

∴ (x – 1)² = 16i²

∴ x² – 2x + 1 = – 16 ...[∵ i² = – 1]

∴ x² – 2x + 17 = 0 ...(i)

x – 1
$x^{2} - 2 x + 17) \bar{x^{3} - 3 x^{2} + 19 x - 20}$
x³ – 2x² + 17x
– + –
– x² + 2x – 20
– x² + 2x – 17x
– + –
– 3

∴ x³ – 3x² + 19x – 20

= (x² – 2x + 17) (x – 1) – 3

= 0(x – 1) – 3 ...[From (i)]

= 0 – 3

∴ x³ – 3x² + 19x – 20 = – 3

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Algebraic Operations of Complex Numbers

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

Q 5) iii)Q 5) ii)Q 6) i)

पाठ 3: Complex Numbers - MISCELLANEOUS EXERCISE - 3 [पृष्ठ ४३]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] 11 Standard Maharashtra State Board

पाठ 3 Complex Numbers
MISCELLANEOUS EXERCISE - 3 | Q 5) iii) | पृष्ठ ४३

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Find the value of: x3 – 3x2 + 19x – 20, if x = 1 – 4i - Mathematics and Statistics

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Find the value of: x3 – 3x2 + 19x – 20, if x = 1 – 4i - Mathematics and Statistics

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