SOLUTION: the value of k for which {{{2x^2+5xy+3y^2+3x+4y+k=0}}}represent a pair of straight lines

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Question 6287: the value of k for which 2x%5E2%2B5xy%2B3y%5E2%2B3x%2B4y%2Bk=0represent a pair of straight lines
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
2x^2+5xy-3y^2+3x+4y+k =0,
Factoring the first three terms, we have
(2x + 3y)(x + y) + 3x + 4y + k = 0
Assume the left polynomial can be factored into
(2x + y+ a)(x + 3y+b) = (2x + 3y)(x + y) + (a+2b)x + (3a+b)y + k
Comparing the coefficients,we have
k = ab and
a+2b = 3 , 3a+b = 4
Solve the system for a,b: we have a = 1 and b = 1
Hence, k = ab = 1
Plz check the answer by yourself.
Kenny