What two numbers multiply to give negative 9 and add to give negative 14?

Answer 1

23

Answer 2

We'll have to use the quadratic formula to solve this, but first we need to get it into a polynomial form.
Let A,B ∈ ℝ
This reads A and B are elements of the real number set, basically just says A and B are real numbers.

First Equation, from "multiply to give negative 9"
AB = -9

Second Equation, from "add to give negative 14"
A + B = -14
A = -B - 14

Plug A, from the second equation, into A in the first equation.
(-B-14)B = -14
B2 + 14B - 9 = 0 <-- this cannot be factored, so we need to use the quadratic formula

B = [-14±√(142-4(1)(-9))]/(2(1))
B = [-14±√(196+36)]/2
B = [-14±√232]/2
B = -7±√58

B = -7+√58 and B = -7-√58
From here, you could plug B back into the first equation to solve for A, however just using the B values:

(-7+√58) x (-7-√58) = -9 (meets one of the conditions)
(-7+√58) + (-7-√58) = -7 + -7 = -14 (meets the other condition)

Therefore your answers are:
-7+√58 and -7-√58