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Algebra

Blazing goIITian

Joined:	1 Feb 2008
Post:	1251

27 Mar 2008 09:40:40 IST

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667

easy

None

If q1 ( x ) = x² + ( k - 29)x - k

and

q2(x) = 2x² + (2k - 43)x + k

are both factors of a cubic polynomial p(x)

then the largest value of k is ??

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Comments (3)

anchit saini

Blazing goIITian

Joined: 1 Feb 2008

Posts: 1251

27 Mar 2008 10:16:29 IST

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please

Hari Shankar

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Joined: 28 Feb 2007

Posts: 2173

27 Mar 2008 12:26:36 IST

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Anchit, if you dont mind i'll just outline the method

The basic thing is to understand that the two quadratics have a common root say

$x^2 + (k-2)x-k = 0\\ 2x^2+(2k-43)x+k = 0$

Put x =

, and eliminate the

term. You get

² in terms of k. Now

0 should give you the answer

Sairam

Blazing goIITian

Joined: 14 Sep 2007

Posts: 573

27 Mar 2008 12:41:20 IST

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Ans is 30

Obviously the 2 quadratics must have a common root

Now ifax^2+bx+C and a'x^2+b'x+c=0 have a common root

(a'c-ac')^2=(bc'-b'c)(ab'-a'b)

apply it here n u get k= 30

the abv formula cn be easily derived

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