**Identify one of the roots of the quadratic equation 25x(x+1) = -4**

A. -1

B. -5/4

C. -1/5

D. -4/3

## Answer: C

**-1/5**

## Solution

25x(x+1) = -4

**Re-arrange the equation be equal to 0**

25x(x+1) + 4 = 0

Expand the bracket

25x² + 25x + 4 = 0

Consider the form **x² + bx + c**

Look for a pair of integers that the **product is c and whose sum is b**. In this case whose **product is 100 and whose sum is 25**

**20, 5**

25x² + 20x + 5x + 4 = 0

(25x² + 20x) + (5x + 4) = 0

5x(5x + 4) + 1(5x + 4) =0

(5x + 4)(5x + 1) = 0

(5x + 4) = 0 or (5x + 1) = 0

For (5x + 4) = 0, we have

5x + 4 = 0

5x = 0 – 4

5x = -4

**x = -4/5**

For (5x + 1) = 0

5x + 1 = 0

5x = 0 -1

5x = -1

**x = -1/5**

**x=-1/5 or x = -4/5**