quadratic

AIEEE Questions › Algebra questions › quadratic

Let f(x)=x²+bx+c,where b,c\in R . If f(x) is a factor of both x⁴+6x²+25 and 3x⁴+4x²+28x+5 , then the least value of f(x) is

#Mathematics #Algebra

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7 Answers

1

chinmay ·2009-03-27 06:29:43

anyone??

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62

Lokesh Verma ·2009-03-27 06:37:50

(x²+5)²-4x²

now try

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chinmay ·2009-03-27 06:44:43

one more hint pls!!

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62

Lokesh Verma ·2009-03-27 06:48:32

(x²+5)²-4x² = (x²+5-2x)(x²+5+2x)

both cannot be factorized further

check which of the two is a factor of the other polynomial!

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341

Hari Shankar ·2009-03-27 07:09:19

Another line of thought:

Let P(x) = x⁴+6x²+25 and Q(x) = 3x⁴+4x²+28x+5

If f(x) divides both P(x) and Q(x),

it must divide 3P(x) - Q(x) = 14(x²+2x+5)

So, f(x)â‰¡x²+2x+5 = (x+1)²+4 â‰¥4

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skygirl ·2009-03-27 07:21:10

simply great!

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Subash ·2009-03-27 07:27:17

prophet sirs posts can be automatically pinked

every post shows so much proficiency :)

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