UPSC CDS I 2025 Mathematics Paper

For a quadratic equation ax2+bx+c=0, if a root is given, substitute it into the equation to find the unknowns.
Calculation:
Substituting the root 2 into the first equation:
‌p(2)2+p(2)+4=0
‌⇒4p+2p+4=0
‌⇒6p+4=0
‌⇒6p=−4
‌⇒p=−‌

2

3

Substituting the root 2 into the second equation:
‌(2)2+q(2)+q=0
‌⇒4+2q+q=0
‌⇒4+3q=0
‌⇒3q=−4
⇒q=−‌

4

3

Now, calculate p+q :
‌p+q=−‌

2

3

−‌

4

3

‌⇒p+q=−‌

6

3

‌⇒p+q=−2