Question

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

Answer 1

Answer:

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  

$P \times (\frac{1}{4} - P ) = -1\\\implies\frac{P}{4} -P^2 = -1\\\implies P - 4P^2 = -4\\\implies 4P^2 -P -4 = 0$

Now, solving this with the help of QUADRATIC Formula:

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

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.