Two numbers when multiplied gives 144 and when added gives -25

Answer 1

so we can make the numbers "a" and "b"

we know that:

a+b= -25

a*b= +144

From this, we can gather that a and b

1. have the same sign
2. are whole numbers

Since they have the same sign an add up to a negative number, they both must be negative.

Now we can just take factors of 144 and add them together.

Pair 1: 2 and 72--> added together they would be 2+72=74. These numbers are too far, we need them closer

Pair 2: 4 and 36 -->added together they would be 4+36=40 These numbers are still a little too far.

Pair 3: 6 and 24 -->added together they would be 6+24=30. Still too far. It's probably the next pair.

Pair 4: 9 and 16-->added together they would be 9+16=25. The sign isn't right though, so we know the true pair is:

-9 and -16.

We can check this:

-9 + - 16 = -25

-9 * -16 = 144

Alternatively, you could turn this into a factoring problem and use the quadratic equation where we make an equation that looks like: (x-a)(x-b)=x^2-25x+144 and then set this to zero. You could also plug this into a graphing calculator and see where the curve crosses the x-axis.