Answer the following: Find the value of x4 + 9x3 + 35x2 − x + 164, if x = −5 + 4i - Mathematics and Statistics

प्रश्न

Answer the following:

Find the value of x⁴ + 9x³ + 35x² − x + 164, if x = −5 + 4i

योग

उत्तर

x = − 5 + 4i

∴ x + 5 = 4i

∴ (x + 5)² = 16i²

∴ x² + 10x + 25 = − 16 ...[∵ i² = − 1]

∴ x² + 10x + 41 = 0 ...(i)

x² − x + 4
∵ $x^{2} + 10 x + 41) \bar{x^{4} + 9 x^{3} + 35 x^{2} - x + 164}$
x⁴ + 10x³ + 41x²
− − −
− x³ − 6x² − x + 164
− x³ − 10x² − 41x
+ + +
4x² + 40x + 164
4x² + 40x + 164
− − −
0

∴ x⁴ + 9x³ + 35x² − x + 164

= (x² + 10x + 41) (x² − x + 4)

= 0(x² − x + 4) ...[From (i)]

∴ x⁴ + 9x³ + 35x² − x + 164 = 0

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Algebraic Operations of Complex Numbers

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q II. (4) (ii)Q II. (4) (i)Q II. (5) (i)

अध्याय 1: Complex Numbers - Miscellaneous Exercise 1.2 [पृष्ठ २२]

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बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board

अध्याय 1 Complex Numbers
Miscellaneous Exercise 1.2 | Q II. (4) (ii) | पृष्ठ २२

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Answer the following: Find the value of x4 + 9x3 + 35x2 − x + 164, if x = −5 + 4i - Mathematics and Statistics

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Answer the following: Find the value of x4 + 9x3 + 35x2 − x + 164, if x = −5 + 4i - Mathematics and Statistics

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