Multiple choice

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

  1. $-1$
  2. $-\dfrac {5}{4}$
  3. $-\dfrac {1}{5}$
  4. $-\dfrac {4}{3}$
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C Correct answer
Explanation

Expanding the equation gives 25x^2 + 25x + 4 = 0. Factoring this quadratic, we get (5x + 1)(5x + 4) = 0, which yields roots x = -1/5 and x = -4/5.

AI explanation

Rewriting the equation in standard quadratic form gives 25x^2 + 25x + 4 = 0. We can factor this quadratic equation by splitting the middle term, yielding 25x^2 + 20x + 5x + 4 = 0. Factoring by grouping gives 5x(5x + 4) + 1(5x + 4) = 0, which leads to (5x + 4)(5x + 1) = 0. Setting the second factor to zero gives 5x + 1 = 0, so x = -1/5.

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