Answer:
The two numbers are 6 and -10
Step-by-step explanation:
Given
[tex]Product = -60[/tex]
[tex]Sum =-4[/tex]
Required
Two numbers that satisfy the above
Let the two numbers be x and y.
So:
[tex]x * y = -60[/tex]
[tex]x + y = -4[/tex]
Make x the subject
[tex]x = -4 - y[/tex]
Substitute [tex]x = -4 - y[/tex] in [tex]x * y = -60[/tex]
[tex](-4 -y) * y = -60[/tex]
Open bracket
[tex]-4y -y^2 = -60[/tex]
Rewrite as:
[tex]y^2 + 4y - 60 = 0[/tex]
Split
[tex]y^2 + 10y - 6y - 60 = 0[/tex]
Factorize
[tex]y(y + 10) - 6(y + 10) = 0[/tex]
Factor out y + 10
[tex](y - 6) (y + 10) = 0[/tex]
Solve for y
[tex]y -6=0\ or\ y+10=0[/tex]
[tex]y =6\ or\ y=-10[/tex]
Recall that:
[tex]x = -4 - y[/tex]
So:
[tex]x = -4-6= -10[/tex]
or
[tex]x = -4--10= 6[/tex]
So:
[tex]y =6\ or\ y=-10[/tex]
[tex]x = -10\ or\ x =6[/tex]
The two numbers are 6 and -10
