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![[Post New]](/templates/default/images/icon_minipost_new.gif) 23 Jul 2007 21:45:57 IST
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if x=1/2(5-  3i) then find value of x4- x3-12x2+ 23x+12, answer should be 5
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23 Jul 2007 22:09:28 IST
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x=(1/2) *(5- 3 i)
=>2x-5=- 3 i
Squaring
=>2x2-10x+11=0
now
x4-x3-12x2+23x-12
=(2x2-10x+11)(1/2 x2+2x+5/4) +(27/2)x-7/4
=(27/2)x-7/4
=(128-27 3i)/4
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~ANSHUMAN
I was born intellegent, education ruined me. |
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23 Jul 2007 22:14:34 IST
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Great work anshuman.
Square the number and make a quadratic equation in x.
Now divide the given polynomial by this quadratic polynomial.
The remainder would be the answer.
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Bipin Kumar Dubey
Chemical Dept.
IIT Kharagpur
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23 Jul 2007 22:19:18 IST
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2x = 5 - root3 i 5-2x = root3 i sq. 25 + 4x2 - 20x = 3i2 4x2 - 20x + 25 = -3 4x2 - 20x + 28 = 0 x2 - 5x + 7 = 0 then divide the given equation by this equation = (x2 - 5x + 7) (x2 + 4x + 1) + remainder as x2 -5x + 7 = 0 so only remainder left = -12 this is the answer hope its rite
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24 Jul 2007 22:01:51 IST
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answer should be 5
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24 Jul 2007 22:50:08 IST
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oopsiieeeeeee yes the answer comes out to b 5.... do the division remainder is 5 only actually didn't noticed 7 , thats y remainder was -12 but its 5 yaar...
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I always like to walk in rain as no one can see me crying there :(
frnds are like diamonds , if u hit them , they don't break but they slip frm ur hands
-----It is better to be hated for what you are than to be loved for what you are not.----
*****wen love and skill work together--expect a masterpiece*****
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