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Mathematics

The solution set for the equation, 25x(x + 1) = -4, is:

  1. {15,45}\Big{\dfrac{1}{5}, \dfrac{4}{5}\Big}

  2. {−15,45}\Big{-\dfrac{1}{5}, \dfrac{4}{5}\Big}

  3. {−45,−15}\Big{-\dfrac{4}{5}, -\dfrac{1}{5}\Big}

  4. {−45,15}\Big{-\dfrac{4}{5}, \dfrac{1}{5}\Big}

Quadratic Equations

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Answer

⇒ 25x(x + 1) = -4

⇒ 25x2 + 25x + 4 = 0

⇒ 25x2 + 5x + 20x + 4 = 0

⇒ 5x(5x + 1) + 4(5x + 1) = 0

⇒ (5x + 4)(5x + 1) = 0

⇒ (5x + 4) = 0 or (5x + 1) = 0      [Using Zero-product rule]

⇒ 5x = -4 or 5x = -1

⇒ x = −45\dfrac{-4}{5} or x = −15\dfrac{-1}{5}.

The solution set: {−45,−15}\Big{-\dfrac{4}{5}, -\dfrac{1}{5}\Big}.

Hence, option 3 is the correct option.

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