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

Answer:

The two numbers are 6 and -10

Step-by-step 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