ax²+bx+c = k(x-alpha)(x-beta), where k is a constant.
=>k[x²-(alpha+beta)X+alpha×beta]
=> kx²-k(alpha+beta)X+k×alpha×beta
comparing the coefficients of x²,X and constant terms we get:
a=k, b=-k(alpha+beta) and c = k×alpha×beta
my question is:
why did he multiplied a constant term? I understand he did it to get the required relationship between the sum and product of the zeroes, but what if k would have been 1? how would he prove the relationship if k would have really been 1??
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yes. you are correct. k is multiplied to maintain a relationship between sum and product of the zeroes.k is a constant as we know. 1 is also a constant. so it works with 1 also...
Amanzn:
how is that possible when k is 1??
that's because a=k, b= -k(alpha+beta) and c=k×alpha×beta
which results in alpha + beta = -b/k or -b/a
and if k is 1, then instead of -b/a, it would be -b..
which is incorrect
Thanks for the help
I got it now, since the value of k can be anything but just for calculation priority k=1 is ignored which is quite right
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