Question

1. Two numbers have a product of 12 but their sum is -7 what are the numbers.

2. The sum of two numbers is 1 but their product is -30 what are the numbers.

Answer 1

Explanation:

hello :

1)Two numbers have a product of 12 but their sum is -7 :

means : xy=12 ....(*)

x+y = -7 ....(**)

solve this system : use (**) you have x = -y-7 put this value in (*)

so : (-y-7)y = 12

-y²-7y-12 = 0

y² +7y+12=0 a=1 b=7 and c= 12

the discriminant delta =b²-4ac delta = 7²-4(1)(12) = 1

y1 = (-7-1)/2 = -4 and y2 = (-7+1)/2 =-3

but x= -7-y

if :y = - 4 x= -7-(-4) =-3

if : y=-3 x = -7-(-3) =-4

2) same method : xy=-30

x+y=1

Answer 2

1. (-3) and (-4)

2. (-5) and 6; vise versa