Question
If $$p$$ and $$q$$ are the roots of the equation $${x^2} + px + q = 0,$$ then
A.
$$p = 1, q = - 2$$
B.
$$p = 0, q = 1$$
C.
$$p = - 2, q = 0$$
D.
$$p = - 2, q = 1$$
Answer :
$$p = 1, q = - 2$$
Solution :
$$\eqalign{
& p + q = - p\,\,{\text{and }}\,pq = q \cr
& \Rightarrow \,\,q\left( {p - 1} \right) = 0 \cr
& \Rightarrow \,\,q = 0\,\,{\text{or }}p = 1. \cr
& {\text{If }}\,q = 0,\,{\text{then }}p = 0.\,\,{\text{i}}{\text{.e}}{\text{.}}\,p = q \cr
& \therefore \,\,p = 1\,\,{\text{and }}q = - 2. \cr} $$