Answer:
The two such fractions are: 113/100 and -22/25.
Explanation:
Let us assume two such fractions are P and Q.
⇒ P x Q = -1
and P + Q = 1/4
Now, to solve for the values of P and Q:
P + Q = 1/4 ⇔ Q = 1/4 - P
Substitute this value of Q in P x Q = -1, we get:
P x Q = -1

Now, solving this with the help of QUADRATIC Formula:

We get: P = 1.13 or P = -0.8825
Now, if P = 1.13, Q = -1/1.13 = -0.88 = -88/100 = -22/25
If P = -0.88, then Q = 1/0.88 = 1.13 = 113/100
Hence, The two such fractions are: 113/100 and -22/25.