## Question:

The square of a negative number is decreased by 14. The resulting number is 5 times the original number. What is the reciprocal of the original number?

A) -1/2

B) -1/4

C) -1/5

D) -1/7

A) -1/2

B) -1/4

C) -1/5

D) -1/7

## Answer:

**A.**

Let x be the negative number.

So,

(-x)^2 - 14 (reduced by 14) = 5x (five times the orginal number, x)

x^2 - 5x -14 = 0.

Solve for the roots.

x = [- b +/- sqrt(b^2 - 4ac)]/2a

x = [5 +/- sqrt(25 + 56)]/2

x = (5 +/- sqrt(81))/2

x = (5 +/- 9)/2

x = -4/2 or x = 14/2

or, x = -2 or x = 7

Since we are talking negative numbers, x = -2 and the reciprocal is -1/2

Hence, the answer is -1/2.