IIT JEE , AIEEE Forum - Mathematics , Algebra

anchitsaini

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 ??

anchitsaini

please

hsbhatt

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

elastiboysai

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