Question

The product of two numbers is 48. The first number is negative, and the second number is four more than twice the first number. Find the two numbers.

Answer 1

If a<0 and the product of a and b is positive, b must also be less than zero.

b=2a+4

ab=48, using b from above

a(2a+4)=48

2a^2+4a=48

2a^2+4a-48=0

2a^2+12a-8a-48=0

2a(a+6)-8(a+6)=0

(2a-8)(a+6)=0, since a<0

a=-6, since b=2a+4

b=-8

So the two numbers are -6 and -8.