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

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

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