Question

If $x+\lambda y-2$ and $x-\mu y+1$ are factors of the expression $6x^2-xy-y^2-6x+8y-12$, then

• A. $\lambda =\frac{1}{3},\mu =\frac{1}{2}$
• B. $\lambda =2,\mu =3$
• C. $\lambda =\frac{1}{3},\mu =-\frac{1}{2}$
• D. $noneofthese$

Answer 1

The correct option is A $\lambda =\frac{1}{3},\mu =\frac{1}{2}$

If $x+\lambda y-2$ and $x-\mu y+1$ are factors of the expression $6x^2-xy-y^2-6x+8y-12$,
Then $a(x+\lambda y-2)(x-\mu y+1)=6x^2-xy-y^2-6x+8y-12$
Equation coefficients, we get, $a=6,a\lambda +2a\mu =8\Rightarrow \lambda +2\mu =\frac{4}{3}$ .... (1)

And $a(\lambda -\mu )=-1\Rightarrow \lambda -\mu =-\frac{1}{6}$ .... (2)
Solving (1) and (2), we get, $\lambda =\frac{1}{3},\mu =\frac{1}{2}$