What two numbers multiply together to equal 12 and add together to equal -5?

Answer 1

7

Answer 2

Let the numbers be m and n.

mn = 12 : therefore n = 12/m

m + n = -5 : substituting for n gives, m + 12/m = -5 :

Multiplying all terms by m gives, m2 + 12 = -5m : m2 + 5m + 12 = 0

Solving for the roots of a quadratic equation, m = [-5 ± √ (52 - 4x12)] ÷ 2 = -2.5 ± i√ 5.75

m = -2.5 + 2.4i and n = -2.5 - 2.4i

CHECK : (-2.5 + 2.4i)(-2.5 - 2.4i) = 6.25 - 5.75i2 = 6.25 + 5.75 = 12

(-2.5 + 2.4i) + (-2.5 - 2.4i) = -5