Explanation:

As p and q are the roots of x²+px+q=0
Then sum of roots = p+q = - p
=>2p + q=0 …….. (i)
Also, product of roots = pq = q
pq − q=0
=> q(p−1)=0
=> p=1or  q=0
If q =0 from (i)
p+q =−p
=>  2p+q=0
=>2p+0=0
=>p=0
Hence p = 0 or 1
Hence option (1)