#1**+10 **

The product of x and y equals -340 and the sum of x and y equals -3

So we have

xy = -340 and

x + y = -3

We can transform the second equation to

y = -3 - x

And putting this into the first equation, we have

x(-3 -x) = -340 simplify

-3x - x^2 = -340 multiply through by -1

x^2 + 3x = 340 subtract 340 from each side

x^2 + 3x - 340 = 0 facror, if possible

(x +20)(x - 17) = 0 set each factor to 0

So

x = -20 and x = 17

And using y = -3 - x

When x = -20, y = -3- (-20) = 17

When x = 17 y = -3 - 17 = -20

So the solutions are (-20, 17) and (17, -20)

CPhill
Apr 3, 2015

#1**+10 **

Best Answer

The product of x and y equals -340 and the sum of x and y equals -3

So we have

xy = -340 and

x + y = -3

We can transform the second equation to

y = -3 - x

And putting this into the first equation, we have

x(-3 -x) = -340 simplify

-3x - x^2 = -340 multiply through by -1

x^2 + 3x = 340 subtract 340 from each side

x^2 + 3x - 340 = 0 facror, if possible

(x +20)(x - 17) = 0 set each factor to 0

So

x = -20 and x = 17

And using y = -3 - x

When x = -20, y = -3- (-20) = 17

When x = 17 y = -3 - 17 = -20

So the solutions are (-20, 17) and (17, -20)

CPhill
Apr 3, 2015

#2**+5 **

Thanks Chris, I am going to show how to do it another way.

your way always works (so long as there really is a solution) , mine only works for whole numbers.

the product of x and y equals -340 and the sum of x and y equals -3

If I am trying to factoize a quadratic and I am expecting integer answers (whole numbers)

**I often use a 'guess' method.**

1) They multiply to a neg number so one is positive and one is negative.

2) They add to a negative so the 'bigger' one is negative.

3) now I more or less forget about the negative signs for a bit.

4) they add to -3 so the numbers are close in value - only 3 apart.

5) Now I am going to look for factors of 340 that suit this.

340 = 34*10 = 2*17*2*5 = 2*2*5*17 = 20*17 that looks helpful, they are 3 apart

6) Must be -20 and +17

Melody
Apr 3, 2015