JEE MAIN - Mathematics (2002 - No. 42)
If $$p$$ and $$q$$ are the roots of the equation $${x^2} + px + q = 0,$$ then
$$p = 1,\,\,q = - 2$$
$$p = 0,\,\,q = 1$$
$$p = - 2,\,\,q = 0$$
$$p = - 2,\,\,q = 1$$
Explanation
$$p + q = - p$$ and $$pq = q \Rightarrow q\left( {p - 1} \right) = 0$$
$$ \Rightarrow q = 0$$ or $$p=1.$$
If $$q = 0,$$ then $$p=0.$$ i.e.$$p=q$$
$$\therefore$$ $$p=1$$ and $$q=-2.$$
$$ \Rightarrow q = 0$$ or $$p=1.$$
If $$q = 0,$$ then $$p=0.$$ i.e.$$p=q$$
$$\therefore$$ $$p=1$$ and $$q=-2.$$
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