What number multiplies to get 30 but adds to get -7?

Answer 1

a+b=-7

rearrange:

b= -a-7=-(a+7)

substitute into:

ab=30

-a(a+7)=30

-a^2-7a-30=0

a^2+7a+30=0

x = complex number, therefore there are no two Real numbers that exist that satisfy these two conditions.

Answer 2

The two numbers are:-(1/2) i (root(71) - 7i)

and:

(1/2) i root(71) + 7i)

Approximate values: a = -3.5 - 4.21307 i, b = -3.5 + 4.21307 i