Complex Numbers And Quadratic Equations question 128
Question: If $ x=-5+2\sqrt{-4}, $ then the value of the expression $ x^{4}+9x^{3}+35x^{2}-x+4 $ is [IIT 1972]
Options:
A) 160
B) $ -160 $
C) 60
D) $ -60 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ x+5=4i $ Þ $ x^{2}+10x+25=-16 $ Now, $ x^{4}+9x^{3}+35x^{2}-x+4 $ $ =(x^{2}+10x+41)(x^{2}-x+4)-160=-160 $
BETA
