Question

Find the value of x² + 9x³ + 35x² – x + 4, if x = -5 + √-4

Answer 1

x = -5 + √-4

x + 5 = √-4

x + 5 = √4 √-1

x + 5 = 2i

(x + 5)² = 4i²

x² + 10x + 25 = 4(-1) ….[∵ i² = -1]

x² + 10x + 29 = 0 …..(i)

Dividend = Divisor × Quotient + Remainder

x⁴ + 9x³ + 35x² – x + 4 = (x² + 10x + 29) (x² – x + 16) – 132x – 460

= 0.(x² – x + 16) – 132x – 460 …..[From (i)]

= -132 (-5 + 2i) – 460

= 660 – 264i – 460 

= 200 – 264i