What two integers can be multiplied to 420 but added together to 1?

To find two integers that multiply to 420 and add up to 1, we can denote these integers as x and y. We have two equations based on the problem:

• x * y = 420
• x + y = 1

From the second equation, we can express y in terms of x:

y = 1 – x

Next, we substitute this expression for y into the first equation:

x * (1 – x) = 420

We can rearrange this into a standard quadratic form:

-x² + x – 420 = 0

Multiplying through by -1 gives us:

x² – x + 420 = 0

Now we can use the quadratic formula, x = (-b ± √(b² – 4ac)) / 2a, where a = 1, b = -1, and c = 420.

Calculating the discriminant:

b² – 4ac = (-1)² – 4(1)(420) = 1 – 1680 = -1679

Since the discriminant is negative, this means that there are no real integer solutions to our equations. Thus, there are no two integers that both multiply to 420 and add to 1.