What two fractions multiply to equal -1 and add to equal 1/4

The two such fractions are: 113/100 and -22/25.

Step-by-step 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.

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