What 2 numbers can you multiply to get 72 and add to get -19?

Answer 1

Let the two numbers be a and b. Then,

ab = 72 therefore b = 72/a. Substituting for b in a + b = -19 gives,

a + 72/a = -19 : multiply both sides by a.

a2 + 72 = -19a : therefore a2 + 19a + 72 = 0

Solving for a quadratic equation gives,

a = [-19 ± √(361 - 288)] ÷ 2 which simplifies to a = -9.5 ± 4.272 (3dp)

The two numbers are therefore -9.5 + 4.272 = -5.228 and -9.5 - 4.272 = -13.772