Find two numbers whose sum is -5 and whose product is -36.

Question

I need to find out the answer to this question

Answer 1

You can work this out by logic by looking at

the products of -36

±1, ±36

±2, ±18

±3, ±12

±4, ±9

±6, ±6

 

From these we can see that -9(4) = -36,  and -9 + 4 = -5

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That being said:  The algebraic method of setting up two

simultaneous equations and solving is as follows:

 

two numbers whose sum is -5 gives us:

equation 1)  x + y = -5

whose product is -36:

equation 2)  xy = -36

 

From equation 1 solve for y in terms of x:

x+y=-5

y = -x-5

 

substitute -x-5 in place of y in equation 2

xy = -36

x(-x-5) = -36

-x² - 5x = -36

Move everything to right side to form a quadratic

by adding x² + 5x to both sides giving:

x²+5x-36 = 0

This can't be factored so solve using quadratic equation

x = [-b ±√(b²-4ac)]/2a      a=1, b=5, c = -36

 

x = [-5±√(5²-4(-36))]/2

x = [-5 ±√169]/2

x = (-5 ± 13)/2

x = (-5+13)/2= 8/2 = 4  OR

x = (-5-13)/2 = -18/2 = -9

 

x = 4, -9

 

Note here that since x+y=-5

For x=4, y=-9

for x = -9, y = 4

 

The two numbers are 4, -9

 

Answer 2

-9 times  4 = -36   and -9 +4 = -5