Question

Find two integers the sum is -13 and the pruduct is 36

Answer 1

Answer:

The integers are -4 and -9

Step-by-step explanation:

Given:

• The sum of the integers = -13
• Product of the integers = 36

To Find:

The integers

Solution:

Let the first integer be x

Let the second integer be y

By given,

Their sum = -13

x + y = -13

x = -13 - y------(1)

Also by given,

Their product = 36

xy = 36

Substitute the value of x

(-13 - y) × y = 36

-13y -y² = 36

y² + 13y + 36 = 0

Factorizing by splitting the middle term,

y² + 9y + 4y + 36 = 0

y (y + 9) + 4 (y + 9) = 0

(y + 9) (y + 4) = 0

Either,

y + 9 = 0

y = -9

Or

y + 4 = 0

y = -4

Case 1:

If y = -9,

x = -13 + 9 = -4

Case 2:

If y = -4

x = -13 + 4 = -9

Hence the integers are -9 and -4.