UPSC CDS 2 2018 Math Paper

1

α+β

=−‌‌

p

9

‌‌

1

α

+‌‌

1

β

=‌‌

α+β

αβ

=−

− q p

‌‌ r p

=−

q

r

−‌‌

1

αβ

=−‌‌

p

r

‌‌

αβ

α+β

=−‌‌

r

q

Since all the fractions are negative, therefore, the smallest ratio of two numbers from p, q and r will produce the largest fraction.
Here p < q < r;thus

p

r

will be minimum.
Hence, the largest fraction is −

p

r

which is equal to −

1

αβ