UPSC CDS Math Quadratic Equations and Inequations Questions

1. a - b < a - c
⇒ -b < - c
⇒ b > c (When an inequality is multiplied or divided by a negative number, the equality changes its sign.)
This is not possible as a negative number cannot be greater than a positive number. Hence, statement 1 is incorrect.
2. a < b
⇒

a

c

<

b

c

(When an inequality is multiplied or divided by a positive number, the equality does not change its sign.)
Hence, statement 2 is correct.
3.

1

b

is a negative real number and

1

c

s a positive real number.
A negative number is less than a positive number.
∴

1

b

<

1

c

Hence, statement 3 is correct