Question

The product of two consecutive negative integers is 600. What is the value of the lesser integer?

A. –60
B. –30
C. –25
D. –15

Answer 1

Answer:

c

Step-by-step explanation:

Answer 2

Given - Product

Find - Integer

Solution - Let the two consecutive integers be x and (x + 1). Representing the given information in mathematical expression form-

$x \times (x + 1) = 600$

Performing multiplication on Left Hand Side

${x}^{2} + x = 600$

Shifting 600 to Left Hand Side

${x}^{2} + x - 600 = 0$

Solving the quadratic equation to find the value of x

x² + 25x - 24x - 600 = 0

x (x + 25) - 24 (x + 25) = 0

(x + 25) (x - 24) = 0

x + 25 = 0

x = - 25

x - 24 = 0

x = 24

As the question mentions, the integers are negative. Hence, one value of x = -25.

Other value of x = x + 1

Other value = -25 + 1

Performing addition of given values as per the sign convention

Other value = -24.

Hence, the two consecutive integers are -24 and -25. The lesser integer is C. –25.