What 2 numbers multiply to equal 3 and add to equal -28?

Question

I need help with this math problem for my homework

Answer 1

Let one number = x

Let the other number = y

 

 

Now we can set two equations using the given information.

 

xy = 3                   eq1

x + y = -28             eq2

 

 

We can substitute eq2 into eq1.  We can get eq1 in terms of x.

 

x(-28 - x) = 3

 

-x² - 28x = 3

 

 

Subtract 3 on both sides of the equation.

 

-x² - 28x - 3 = 0

 

 

We have here a quadratic equation.  Therefore, we can use the quadratic formula to solve for x.

 

x = (-b ± √(b² - 4ac)) / 2a

 

where:

a = -1

b = -28

c = -3

 

 

x = (28 ± √(784 - 4(3))) / -2

x = (28 ± √(772)) / -2

x = (28 ± 27.785) / -2

 

x = (28 - 27.785) / -2                  and                x = (28 + 27.785) / -2

 

x = -0.108                                 and                  x = -27.893

 

 

Substitute these x values into eq2 to solve for y.

 

y = -28 - (-0.108)                   y = -28 - (-27.893)

y = -27.892                            y = -0.107

 

 

We have two pairs of solutions.

 

x = -0.108                                x = -27.893

y = -27.892                              y = -0.107

 

 

Both pairs work out.

 

 

Answer 2

let x and y be the numbers

xy=3 and x+y=-28

x+y=-28 implies x=-y-28

substitute

y(-y-28)=3

-y^2-28y=3

y^2+28y+3=0

using the quadratic formula...

[-28±√(784-12)]/2

[-28±√772]/2   (772=4*193)

[-28±2√193]/2

-14+√193 and -14-√193 are the two numbers

add and the radicals cancel and you get -14+(-14)=-28

multiply and you get (-14)(-14)-(√193)^2=196-193=3

Answer 3

Do you mean what two numbers multiply to equal -28 and add to 3?
If this is the case, the question has a solution:

first, what are the factors of 28? (we will ignore the negative for just a moment)

 

you've got 1 and 28, 2 and 14, 4 and 7.

 

Now, in each of those pairs of numbers one of the numbers has to be negative because the final product is negative. A positive number multiplied by a negative number is always negative.

So, finally of the three pairs of numbers, which one will add up to equal 3?
For example, if you choose 2 and 14, decide which one is negative. Let's say that the 2 is negative. So, -2 + 14 = 12.
See if you can figure it out. :)

Answer 4

let them be x and y 

so x+y= -28 and xy=3

 

x+ 3/x=-28

 

x²+ 28 x+3=0

 

(x+14)²=193

 

x= -14 ±√193