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Algebra

Cool goIITian

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16 Apr 2010 15:39:17 IST

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1) If a,b are the roots of the equation x^2- 2x+8=0 , then the value(a^2/b)^1/3 + (b^2/a)^1/3 is eq

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1) If a,b are the roots of the equation x^2- 2x+8=0 , then the value(a^2/b)^1/3 + (b^2/a)^1/3 is equal to2)If |z1| = 1, |z2| = 2, |z3|= 3and |9z1z2+4z1z3+z2z3| = 12 , then the value of |z1+z2+z3| is equal to3) If the equation ax2+ bx + c = 0, 0 < a < b < c, has non real complex roots z1 and z2 then a)|z1| > 1, |z2| < 1 b)|z1| < 1, |z2| < 1 c)|z1| < 1, |z2| > 1 d)|z1| > 1, |z2| > 1

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Sujit

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16 Apr 2010 17:10:02 IST

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a^2/3/b^1/3+b^2/3/a^1/3=(a+b)/ab^1/3=2/8^1/3=1

Sujit

Blazing goIITian

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16 Apr 2010 17:16:14 IST

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.... ' means bar

|Z₁+Z₂+Z₃|=| Z₁'+ Z₂'+ Z₃' |=| 1/Z₁+4/Z₂ +9/Z₃|=12/|Z₁|*|Z₂|*|Z₃|=2

Sujit

Blazing goIITian

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16 Apr 2010 17:18:09 IST

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qus 3 is unclear could u pls type it once again

pragya

Cool goIITian

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16 Apr 2010 17:46:37 IST

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3) If the equation ax2+ bx + c = 0, 0 < a < b < c, has non real complex roots z1 and z2 then which is true a)|z1| > 1, |z2| < 1 b)|z1| < 1, |z2| < 1 c)|z1| < 1, |z2| > 1 d)|z1| > 1, |z2| > 1

Sujit

Blazing goIITian

Joined: 11 Mar 2009

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16 Apr 2010 18:04:14 IST

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3. i was unable to reach the final answer

BUT options A and C are wrong as the two ro0ts are conjugate and as we know |Z|=|Z'|

as as mentioned non-real complex roots

b²<4ac

=> (b/a)²<4c/a

=> (z+z')²<4z * z'

=> re(z)²<re(z)² +im(z)²

and after this i m unable to proceed ...and hope the xperts come to rescue

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