Question

Find two numbers that multiply to -24 and adds to 2

Answer 1

6 and -4

Explanation:

Let the first number be n.

Other number=
`(-24)/(n)`

Their sum= 2

n +
`(-24)/(n)`= 2

`(n^(2-24) )/(n)`= 2

n²-24= 2n

You can solve this problem in either of these 2 ways:

i) Square Completion method:

n²-2n = 24

Half of the coefficient=
`(2)/(2)` =1

Its square= 1²= 1

n²-2n+1= 24+1

(n-1)²= 25

n-1=
`√(25)`

n-1= ±5

If n-1= 5,

n= 5+1

n= 6

If n-1= -5,

n= -5+1

n= -4

∴ the numbers are 6 and -4

ii) Equation Method:

n²-24= 2n

n²-2n-24= 0

a= 1,

b= -2,

-b= 2,

c= -24

n= -b±
`\sqrt{b^(2)-4ac }`/2a

n= 2±
`\sqrt{-2^(2)-4x1x-24`/2x1

n= 2±
`√(4+96)`/2

n= 2±
`√(100)`/2

n= 2±10/2

If n=
`(2+10)/(2)`,

n=
`(12)/(2)`

n= 6

If n=
`(2-10)/(2)`,

n=
`(-8)/(2)`

n= -4

∴ the numbers are 6 and -4