UPSC NDA Math Model Paper 6

For the quadratic equation: x + px + q = 0, it is given that p and q are its root.
As well as for the given quadratic equation: we have, a = 1, b = p and c = q.
⇒ Sum of the roots = -b/a
⇒ p + q = - p .......(1)
⇒ Product of the roots = c/a
⇒ pq = q
⇒ pq - q = 0
⇒ q (p - 1) = 0
⇒ q = 0 or p = 1.
Case-1:
If q = 0, then p = 0. i.e. p = q = 0 (By substituting value of p in equation 1)
Case-2:
If p = 1, then q = -2 (By substituting value of p in equation 1)