1.

The value(s) of m for which the expression `2x^2+mxy+3y^2-5y-2` can be factorized in to two linear factors are:

Answer» `3y^2+y(mx-5)+2x^2-2`
`a=3,b=mx-5,c=2x^2-2`
`b^2-4ac=(mx-5)^2-4*3(2x^2-2)`
`m^2x^2+25-10mn-24x^2+24`
`x^2(m^2-24)-10mx+49`
`(m^2-24)x^2-2*7(5mn)/7+7^2`
`(2*7(5m)/7)^2=4*(m^2-24)*7^2`
`25m^2=49m^2-49*24`
`m^2=49`
`m=pm7`.


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