Question
If $$x + \lambda y - 2$$ and $$x - \mu y + 1$$ are factors of the expression $$6{x^2} - xy - {y^2} - 6x + 8y - 12$$ 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.
None of these
Answer :
$$\lambda = \frac{1}{3},\mu = \frac{1}{2}$$
Solution :
$$6{x^2} - xy - {y^2} - 6x + 8y - 12 = 6\left( {x + \lambda y - 2} \right)\left( {x - \mu y + 1} \right).$$
Equate co-efficients and solve for $$\lambda ,\mu .$$