UPSC CDS I 2025 Mathematics Paper

Let α and β be the roots of the equation:
‌α+β=−p
‌α⋅β=q
But it's given that roots are p and q themselve
‌p+q=−p
‌p×q=q.
Calculations:
From (ii): p×q=q
Divide both sides by q (since q≠0 ):
⇒p=1
Substitute p=1 into (i):
⇒1+q=−1⇒q=−2
Now find: p2+q2
=12+(−2)2=1+4=5