Home
Class 12
MATHS
Find the value of m for which the expres...

Find the value of `m` for which the expressiion `12x^(2)-10xy+2y^(2)+11x-5y+m` can be resolved into two rational linear factors.

Text Solution

Verified by Experts

Comparing the given expression with
`ax^(2)+2hxy+by^(2)_2gx+2fy+c`, we have
`a=12, h=-5, b=2, g=11/2,f=(-5/2),c=m`
The given expression will have two linear factors if and only if
`abc+2fgh-af^(2)-bg^(2)-ch^(2)=0`
or `(12)(2)(m)(-5/2)(11/2)(-5)-(12)(-5/2)^(2)`
`-(2)(11/2)^(2)-(m)(-5)^(2)=0`
`implies24m+275/2-75-121/2-25m=0` or `m-2`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the values of m for which the expression 2x^2+m x y+3y^2-5y-2 can be resolved into two rational linear factors.

For what value of lambda does the equation 12x^2-10xy+2y^2+11x-5y+lambda=0 represent a pair of straight lines ? Find their equations and the angle between them.

Find the value of k for which the pair of linear equations 2x-3y=12 and 6x+ky=36 has infinitely many solutions.

Find the linear factors of x^(2)-5xy+4y^(2)+x+2y-2

Find the real value of m for which the substitution y=u^m will transform the differential equation 2x^4y(dy)/(dx)+y^4=4x^6 in to a homogeneous equation.

Find the new equation of curve 12x^2+7xy-12y^2-17x-31y-7=0 after removing the first degree terms.

The value of m for which straight line 3x-2y+z+3=0=4x-3y+4z+1 is parallel to the plane 2x-y+mz-2=0 is

Find the point of inersection of lines represented by 2x^2-7xy-4y^2-x+22y-10=0

The values of lambda for which the system of equations x+y+z=6,x+2y+3z=10, x+2y+lambdaz=12 is inconsistent

Find the value of x and y from the equation. [{:(3x+7,5),(y+1,2-3x):}]=[{:(-2,5),(1,11):}]