Question

Write two numbers that multiply to the value on top and add to the value on bottom. -60−60 -4−4 \times× ++

Answer 1

The two numbers are 6 and -10

Explanation:

Given

`Product = -60`

`Sum =-4`

Required

Two numbers that satisfy the above

Let the two numbers be x and y.

So:

`x * y = -60`

`x + y = -4`

Make x the subject

`x = -4 - y`

Substitute
`x = -4 - y` in
`x * y = -60`

`(-4 -y) * y = -60`

Open bracket

`-4y -y^2 = -60`

Rewrite as:

`y^2 + 4y - 60 = 0`

Split

`y^2 + 10y - 6y - 60 = 0`

Factorize

`y(y + 10) - 6(y + 10) = 0`

Factor out y + 10

`(y - 6) (y + 10) = 0`

Solve for y

`y -6=0\ or\ y+10=0`

`y =6\ or\ y=-10`

Recall that:

`x = -4 - y`

So:

`x = -4-6= -10`

or

`x = -4--10= 6`

So:

`y =6\ or\ y=-10`

`x = -10\ or\ x =6`

The two numbers are 6 and -10