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# The value of k for which the expression x2+2xy+ky2 +2x+k = 0 can be resolved into 2 linear factors is given by?

9 years ago

this is an equation of second degree. if this equation can be resolved into linear factors, the linear factors will represent two straight lines which means the given equation should be pair of straight lines.

for pair of straight lines, Δ =0

comparing given equation with ax2 + 2hxy + by2 + 2gx + 2fy + c =0

putting  Δ = abc+2fgh-af2-bg2-ch2 = 0

k2-2k = 0

k(k-2)=0

k=0 or k=2

regards

Nikhil

9 years ago

i posted answer with respect to context of coordinate geometry, and its there in 11th syllabus. if u are confused on Δ then its very useful concept , u must learn it.

9 years ago

general equation of second degree is given as

ax2 + 2hxy + by2 + 2gx + 2fy + c =0

this equation may represent any conic section under different conditions. so, we define Δ here.

Δ = abc+2fgh-af2-bg2-ch2 = 0

Conditions equation of the conic represents

Δ=0                                                    pair of straight lines

h=0 , a=b                                              circle

Δ≠0 ,h2-ab=0                                          parabola

Δ≠0, h2-ab<0                                             ellipse

Δ≠0, h2-ab>0                                             hyperbola

Δ≠0, h2-ab>0 , a+b=0                                   rectangular hyperbola